We show that equivariant Donaldson polynomials of compact toric surfaces can be calculated as residues of suitable combinations of Virasoro conformal blocks, by building on AGT correspondence between $\mathcal{N}=2$ supersymmetric gauge theories and two-dimensional conformal field theory. Talk presented by A.T. at the conference Interactions between Geometry and Physics — in honor of Ugo Bruzzo’s 60th birthday 17–22 August 2015, Guarujá, São Paulo, Brazil, mostly based on Bawane et al. (0000) and Bershtein et al. (0000).

%B Journal of Geometry and Physics %V 118 %P 40 - 50 %G eng %U http://www.sciencedirect.com/science/article/pii/S0393044017300165 %R https://doi.org/10.1016/j.geomphys.2017.01.012 %0 Journal Article %J Journal of High Energy Physics %D 2017 %T Real topological string amplitudes %A Narain, K. S. %A Nicolò Piazzalunga %A Alessandro Tanzini %XWe discuss the physical superstring correlation functions in type I theory (or equivalently type II with orientifold) that compute real topological string amplitudes. We consider the correlator corresponding to holomorphic derivative of the real topological amplitude $\mathcal{G_\chi}$, at fixed worldsheet Euler characteristic $\chi$. This corresponds in the low-energy effective action to $\mathcal{N}=2$ Weyl multiplet, appropriately reduced to the orientifold invariant part, and raised to the power $g'= −\chi+ 1$. We show that the physical string correlator gives precisely the holomorphic derivative of topological amplitude. Finally, we apply this method to the standard closed oriented case as well, and prove a similar statement for the topological amplitude $\mathcal{F}_g$.

%B Journal of High Energy Physics %V 2017 %P 80 %8 Mar %G eng %U https://doi.org/10.1007/JHEP03(2017)080 %R 10.1007/JHEP03(2017)080 %0 Journal Article %J Journal of High Energy Physics %D 2016 %T Exact results for N=2 supersymmetric gauge theories on compact toric manifolds and equivariant Donaldson invariants %A Mikhail Bershtein %A Giulio Bonelli %A Massimiliano Ronzani %A Alessandro Tanzini %XWe provide a contour integral formula for the exact partition function of $\mathcal{N}=2$ supersymmetric $U(N)$ gauge theories on compact toric four-manifolds by means of supersymmetric localisation. We perform the explicit evaluation of the contour integral for $U(2)\; \mathcal{N}=2^\star$ theory on $\mathbb{P}^2$ for all instanton numbers. In the zero mass case, corresponding to the $\mathcal{N}=4$ supersymmetric gauge theory, we obtain the generating function of the Euler characteristics of instanton moduli spaces in terms of mock-modular forms. In the decoupling limit of infinite mass we find that the generating function of local and surface observables computes equivariant Donaldson invariants, thus proving in this case a longstanding conjecture by N. Nekrasov. In the case of vanishing first Chern class the resulting equivariant Donaldson polynomials are new.

%B Journal of High Energy Physics %V 2016 %P 23 %8 Jul %G eng %U https://doi.org/10.1007/JHEP07(2016)023 %R 10.1007/JHEP07(2016)023 %0 Journal Article %J Journal of High Energy Physics %D 2016 %T Symmetry enhancements via 5d instantons, qW-algebrae and (1,0) superconformal index %A Benvenuti, Sergio %A Giulio Bonelli %A Massimiliano Ronzani %A Alessandro Tanzini %XWe explore $\mathcal{N}=(1,0)$ superconformal six-dimensional theories arising from M5 branes probing a transverse $A_k$ singularity. Upon circle compactification to 5 dimensions, we describe this system with a dual pq-web of five-branes and propose the spectrum of basic five-dimensional instanton operators driving global symmetry enhancement. For a single M5 brane, we find that the exact partition function of the 5d quiver gauge theory matches the 6d (1, 0) index, which we compute by letter counting. We finally show that S-duality of the pq-web implies new relations among vertex correlators of $q\mathcal{W}$ algebrae.

%B Journal of High Energy Physics %V 2016 %P 53 %8 Sep %G eng %U https://doi.org/10.1007/JHEP09(2016)053 %R 10.1007/JHEP09(2016)053 %0 Journal Article %J Journal of High Energy Physics %D 2015 %T N=2 supersymmetric gauge theories on S^2xS^2 and Liouville Gravity %A Aditya Bawane %A Giulio Bonelli %A Massimiliano Ronzani %A Alessandro Tanzini %XWe consider $\mathcal{N}=2$ supersymmetric gauge theories on four manifolds admitting an isometry. Generalized Killing spinor equations are derived from the consistency of supersymmetry algebrae and solved in the case of four manifolds admitting a $U(1)$ isometry. This is used to explicitly compute the supersymmetric path integral on $S^2 \times S^2$ via equivariant localization. The building blocks of the resulting partition function are shown to contain the three point functions and the conformal blocks of Liouville Gravity.

%B Journal of High Energy Physics %V 2015 %P 54 %8 Jul %G eng %U https://doi.org/10.1007/JHEP07(2015)054 %R 10.1007/JHEP07(2015)054 %0 Journal Article %D 2014 %T Six-dimensional supersymmetric gauge theories, quantum cohomology of instanton moduli spaces and gl(N) Quantum Intermediate Long Wave Hydrodynamics %A Giulio Bonelli %A Antonio Sciarappa %A Alessandro Tanzini %A Petr Vasko %X We show that the exact partition function of U(N) six-dimensional gauge theory with eight supercharges on C^2 x S^2 provides the quantization of the integrable system of hydrodynamic type known as gl(N) periodic Intermediate Long Wave (ILW). We characterize this system as the hydrodynamic limit of elliptic Calogero-Moser integrable system. We compute the Bethe equations from the effective gauged linear sigma model on S^2 with target space the ADHM instanton moduli space, whose mirror computes the Yang-Yang function of gl(N) ILW. The quantum Hamiltonians are given by the local chiral ring observables of the six-dimensional gauge theory. As particular cases, these provide the gl(N) Benjamin-Ono and Korteweg-de Vries quantum Hamiltonians. In the four dimensional limit, we identify the local chiral ring observables with the conserved charges of Heisenberg plus W_N algebrae, thus providing a gauge theoretical proof of AGT correspondence. %I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34546 %1 34771 %2 Physics %4 2 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-09-28T10:16:32Z No. of bitstreams: 1 art2014.pdf: 600092 bytes, checksum: 8a020f470fff4ce83b5d820436def73f (MD5) %R 10.1007/JHEP07(2014)141 %0 Journal Article %D 2014 %T The stringy instanton partition function %A Giulio Bonelli %A Antonio Sciarappa %A Alessandro Tanzini %A Petr Vasko %X We perform an exact computation of the gauged linear sigma model associated to a D1-D5 brane system on a resolved A_1 singularity. This is accomplished via supersymmetric localization on the blown-up two-sphere. We show that in the blow-down limit C^2/Z_2 the partition function reduces to the Nekrasov partition function evaluating the equivariant volume of the instanton moduli space. For finite radius we obtain a tower of world-sheet instanton corrections, that we identify with the equivariant Gromov-Witten invariants of the ADHM moduli space. We show that these corrections can be encoded in a deformation of the Seiberg-Witten prepotential. From the mathematical viewpoint, the D1-D5 system under study displays a twofold nature: the D1-branes viewpoint captures the equivariant quantum cohomology of the ADHM instanton moduli space in the Givental formalism, and the D5-branes viewpoint is related to higher rank equivariant Donaldson-Thomas invariants of P^1 x C^2. %I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34589 %1 34796 %2 Physics %4 2 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-09-28T14:48:41Z No. of bitstreams: 1 art2014.pdf: 719350 bytes, checksum: 2c296ad8eb7995f07c16f6d4e36c6813 (MD5) %R 10.1007/JHEP01(2014)038 %0 Journal Article %D 2014 %T Vortex Partition Functions, Wall Crossing and Equivariant Gromov–Witten Invariants %A Giulio Bonelli %A Antonio Sciarappa %A Alessandro Tanzini %A Petr Vasko %X In this paper we identify the problem of equivariant vortex counting in a (2,2) supersymmetric two dimensional quiver gauged linear sigma model with that of computing the equivariant Gromov–Witten invariants of the GIT quotient target space determined by the quiver. We provide new contour integral formulae for the I and J-functions encoding the equivariant quantum cohomology of the target space. Its chamber structure is shown to be encoded in the analytical properties of the integrand. This is explained both via general arguments and by checking several key cases. We show how several results in equivariant Gromov–Witten theory follow just by deforming the integration contour. In particular, we apply our formalism to compute Gromov–Witten invariants of the C3/Zn orbifold, of the Uhlembeck (partial) compactification of the moduli space of instantons on C2, and of An and Dn singularities both in the orbifold and resolved phases. Moreover, we analyse dualities of quantum cohomology rings of holomorphic vector bundles over Grassmannians, which are relevant to BPS Wilson loop algebrae. %I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34652 %1 34859 %2 Physics %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-10-20T12:25:03Z No. of bitstreams: 1 preprint2014.pdf: 652465 bytes, checksum: 355132ee06625045b6adf8b1f4862533 (MD5) %R 10.1007/s00220-014-2193-8 %0 Report %D 2013 %T N=2 gauge theories on toric singularities, blow-up formulae and W-algebrae %A Giulio Bonelli %A Kazunobu Maruyoshi %A Alessandro Tanzini %A Futoshi Yagi %X We compute the Nekrasov partition function of gauge theories on the\r\n(resolved) toric singularities C^2/\\Gamma in terms of blow-up formulae. We\r\ndiscuss the expansion of the partition function in the \\epsilon_1,\\epsilon_2\r\n\\to 0 limit along with its modular properties and how to derive them from the\r\nM-theory perspective. On the two-dimensional conformal field theory side, our\r\nresults can be interpreted in terms of representations of the direct sum of\r\nHeisenberg plus W_N-algebrae with suitable central charges, which can be\r\ncomputed from the fan of the resolved toric variety.We provide a check of this\r\ncorrespondence by computing the central charge of the two-dimensional theory\r\nfrom the anomaly polynomial of M5-brane theory. Upon using the AGT\r\ncorrespondence our results provide a candidate for the conformal blocks and\r\nthree-point functions of a class of the two-dimensional CFTs which includes\r\nparafermionic theories. %I SISSA %G en %U http://hdl.handle.net/1963/6577 %1 6522 %2 Mathematics %4 -1 %$ Submitted by Alessandro Tanzini (tanzini@sissa.it) on 2013-04-04T10:00:01Z\nNo. of bitstreams: 1\n1208.0790v4.pdf: 372527 bytes, checksum: 5fae7067b646df2fca0b20daa82b5cff (MD5) %0 Journal Article %J Lett. Math. Phys. 101 (2012) 103-124 %D 2012 %T Gauge Theories on ALE Space and Super Liouville Correlation Functions %A Giulio Bonelli %A Kazunobu Maruyoshi %A Alessandro Tanzini %X We present a relation between N=2 quiver gauge theories on the ALE space O_{P^1}(-2) and correlators of N=1 super Liouville conformal field theory, providing checks in the case of punctured spheres and tori. We derive a blow-up formula for the full Nekrasov partition function and show that, up to a U(1) factor, the N=2^* instanton partition function is given by the product of the character of \\\\hat{SU}(2)_2 times the super Virasoro conformal block on the torus with one puncture. %B Lett. Math. Phys. 101 (2012) 103-124 %I SISSA %G en %U http://hdl.handle.net/1963/4305 %1 4068 %2 Physics %3 Elementary Particle Theory %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-28T07:00:50Z\\r\\nNo. of bitstreams: 1\\r\\n1107.4609v1.pdf: 256160 bytes, checksum: f34c8fc8ed919adff7b4d65312b81db1 (MD5) %R 10.1007/s11005-012-0553-x %0 Journal Article %J JHEP 06(2012)178 %D 2012 %T Vertices, vortices & interacting surface operators %A Giulio Bonelli %A Alessandro Tanzini %A Zhao Jian %X We show that the vortex moduli space in non-abelian supersymmetric N=(2,2) gauge theories on the two dimensional plane with adjoint and anti-fundamental matter can be described as an holomorphic submanifold of the instanton moduli space in four dimensions. The vortex partition functions for these theories are computed via equivariant localization. We show that these coincide with the field theory limit of the topological vertex on the strip with boundary conditions corresponding to column diagrams. Moreover, we resum the field theory limit of the vertex partition functions in terms of generalized hypergeometric functions formulating their AGT dual description as interacting surface operators of simple type. Analogously we resum the topological open string amplitudes in terms of q-deformed generalized hypergeometric functions proving that they satisfy appropriate finite difference equations. %B JHEP 06(2012)178 %I SISSA %G en %U http://hdl.handle.net/1963/4134 %1 3874 %2 Physics %3 Elementary Particle Theory %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-15T08:59:30Z\\r\\nNo. of bitstreams: 1\\r\\n1102.0184v1.pdf: 250685 bytes, checksum: b0209b95cc58d31e3cd28c41cd8b0f25 (MD5) %R 10.1007/JHEP06(2012)178 %0 Journal Article %J JHEP 02(2012)031 %D 2012 %T Wild quiver gauge theories %A Giulio Bonelli %A Kazunobu Maruyoshi %A Alessandro Tanzini %XWe study $N=2$ supersymmetric $SU(2)$ gauge theories coupled to non-Lagrangian superconformal field theories induced by compactifying the six dimensional $A_1 (2,0)$ theory on Riemann surfaces with irregular punctures. These are naturally associated to Hitchin systems with wild ramification whose spectral curves provide the relevant Seiberg-Witten geometries. We propose that the prepotential of these gauge theories on the Omega-background can be obtained from the corresponding irregular conformal blocks on the Riemann surfaces via a generalization of the coherent state construction to the case of higher order singularities.

%B JHEP 02(2012)031 %I SISSA %G en %U http://hdl.handle.net/1963/5184 %1 4999 %2 Physics %3 Elementary Particle Theory %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-12-12T14:57:36Z\\r\\nNo. of bitstreams: 1\\r\\n1112.1691v1.pdf: 374306 bytes, checksum: d108d1f4f381124a4ff917b4c621f359 (MD5) %R 10.1007/JHEP02(2012)031 %0 Journal Article %J JHEP, Volume 2011, Issue 7, 2011, Article number055 %D 2011 %T Generalized matrix models and AGT correspondence at all genera %A Giulio Bonelli %A Kazunobu Maruyoshi %A Alessandro Tanzini %A Futoshi Yagib %X We study generalized matrix models corresponding to n-point Virasoro\r\nconformal blocks on Riemann surfaces with arbitrary genus g. Upon AGT\r\ncorrespondence, these describe four dimensional N=2 SU(2)^{n+3g-3} gauge\r\ntheories with generalized quiver diagrams. We obtain the generalized matrix\r\nmodels from the perturbative evaluation of the Liouville correlation functions\r\nand verify the consistency of the description with respect to degenerations of\r\nthe Riemann surface. Moreover, we derive the Seiberg-Witten curve for the N=2\r\ngauge theory as the spectral curve of the generalized matrix model, thus\r\nproviding a check of AGT correspondence at all genera. %B JHEP, Volume 2011, Issue 7, 2011, Article number055 %I SISSA %G en %U http://hdl.handle.net/1963/6568 %1 6530 %2 Mathematics %4 1 %$ Submitted by Alessandro Tanzini (tanzini@sissa.it) on 2013-04-04T10:07:44Z\nNo. of bitstreams: 1\n1011.5417v2.pdf: 288213 bytes, checksum: 4ffb3884bb05de0280c0f8a0dc7847ab (MD5) %R 10.1007/JHEP07(2011)055 %0 Report %D 2011 %T Instantons on ALE spaces and Super Liouville Conformal Field Theories %A Giulio Bonelli %A Kazunobu Maruyoshi %A Alessandro Tanzini %X We provide evidence that the conformal blocks of N=1 super Liouville\\r\\nconformal field theory are described in terms of the SU(2) Nekrasov partition\\r\\nfunction on the ALE space O_{P^1}(-2). %I SISSA %G en %U http://hdl.handle.net/1963/4262 %1 3987 %2 Physics %3 Elementary Particle Theory %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-26T14:31:56Z\\nNo. of bitstreams: 1\\n1106.2505v1.pdf: 137191 bytes, checksum: 721cf25d724b7aca87a3429a0119e201 (MD5) %0 Journal Article %J JHEP 09(2011)096 %D 2011 %T The Liouville side of the vortex %A Giulio Bonelli %A Alessandro Tanzini %A Jian Zhao %X We analyze conformal blocks with multiple (semi-)degenerate field insertions in Liouville/Toda conformal field theories an show that their vector space is fully reproduced by the four-dimensional limit of open topological string amplitudes on the strip with generic boundary conditions associated to a suitable quiver gauge theory. As a byproduct we identify the non-abelian vortex partition function with a specific fusion channel of degenerate conformal blocks. %B JHEP 09(2011)096 %I SISSA %G en %U http://hdl.handle.net/1963/4304 %1 4019 %2 Physics %3 Elementary Particle Theory %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-27T09:53:04Z\\r\\nNo. of bitstreams: 1\\r\\n1107.2787v1.pdf: 990433 bytes, checksum: 1dc28192f585097bc1e32987afd97aa7 (MD5) %R 10.1007/JHEP09(2011)096 %0 Journal Article %J Communications in Mathematical Physics 304 (2011) 395-409 %D 2011 %T Poincaré polynomial of moduli spaces of framed sheaves on (stacky) Hirzebruch surfaces %A Ugo Bruzzo %A Rubik Poghossian %A Alessandro Tanzini %XWe perform a study of the moduli space of framed torsion-free sheaves on Hirzebruch surfaces by using localization techniques. We discuss some general properties of this moduli space by studying it in the framework of Huybrechts-Lehn theory of framed modules. We classify the fixed points under a toric action on the moduli space, and use this to compute the Poincare polynomial of the latter. This will imply that the moduli spaces we are considering are irreducible. We also consider fractional first Chern classes, which means that we are extending our computation to a stacky deformation of a Hirzebruch surface. From the physical viewpoint, our results provide the partition function of N=4 Vafa-Witten theory on total spaces of line bundles on P1, which is relevant in black hole entropy counting problems according to a conjecture due to Ooguri, Strominger and Vafa.

%B Communications in Mathematical Physics 304 (2011) 395-409 %I Springer %V 304 %P 395-409 %8 06/2011 %G en_US %U http://hdl.handle.net/1963/3738 %N 2 %1 579 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-09-09T09:26:43Z\\r\\nNo. of bitstreams: 1\\r\\nBPT-8.pdf: 250954 bytes, checksum: 984c30f0144339468a97f54d6b22ce05 (MD5) %R 10.1007/s00220-011-1231-z %0 Report %D 2011 %T Quantum Hitchin Systems via beta-deformed Matrix Models %A Giulio Bonelli %A Kazunobu Maruyoshi %A Alessandro Tanzini %XWe study the quantization of Hitchin systems in terms of beta-deformations of generalized matrix models related to conformal blocks of Liouville theory on punctured Riemann surfaces. We show that in a suitable limit, corresponding to the Nekrasov-Shatashvili one, the loop equations of the matrix model reproduce the Hamiltonians of the quantum Hitchin system on the sphere and the torus with marked points. The eigenvalues of these Hamiltonians are shown to be the epsilon1-deformation of the chiral observables of the corresponding N=2 four ndimensional gauge theory. Moreover, we find the exact wave-functions in terms of the matrix model representation of the conformal blocks with degenerate field insertions.

%I SISSA %G en %U http://hdl.handle.net/1963/4181 %1 3904 %2 Physics %3 Elementary Particle Theory %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-22T10:22:35Z\\nNo. of bitstreams: 1\\n1104.4016v2.pdf: 317021 bytes, checksum: 92bcb534e0e6fdeb2e5c51517f28d510 (MD5) %0 Journal Article %J J. Geom. Phys. 60 (2010) 417-429 %D 2010 %T Chern-Simons theory on L(p,q) lens spaces and Gopakumar-Vafa duality %A Andrea Brini %A Luca Griguolo %A Domenico Seminara %A Alessandro Tanzini %X We consider aspects of Chern-Simons theory on L(p,q) lens spaces and its relation with matrix models and topological string theory on Calabi-Yau threefolds, searching for possible new large N dualities via geometric transition for non-SU(2) cyclic quotients of the conifold. To this aim we find, on one hand, some novel matrix integral representations of the SU(N) CS partition function in a generic flat background for the whole L(p,q) family and provide a solution for its large N dynamics; on the other, we perform in full detail the construction of a family of would-be dual closed string backgrounds via conifold geometric transition from T^*L(p,q). We can then explicitly prove that Gopakumar-Vafa duality in a fixed vacuum fails in the case q>1, and briefly discuss how it could be restored in a non-perturbative setting. %B J. Geom. Phys. 60 (2010) 417-429 %G en_US %U http://hdl.handle.net/1963/2938 %1 1762 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-12T16:01:18Z\\nNo. of bitstreams: 1\\n0809.1610v1.pdf: 287875 bytes, checksum: feadff501b37135585a6f62946b628de (MD5) %R 10.1016/j.geomphys.2009.11.006 %0 Journal Article %J Phys. Lett. B 691 (2010) 111-115 %D 2010 %T Hitchin systems, N=2 gauge theories and W-gravity %A Giulio Bonelli %A Alessandro Tanzini %X We propose some arguments supporting an M-theory derivation of the duality recently discovered by Alday, Gaiotto and Tachikawa between two-dimensional conformal field theories and N=2 superconformal gauge theories in four dimensions. We find that A_{N-1} Toda field theory is the simplest two-dimensional conformal field theory quantizing the moduli of N M5-branes wrapped on a Riemann surface. This leads us to identify chiral operators of the N=2 gauge theories with W-algebra currents. As a check of this correspondence we study some relevant OPE\\\'s obtaining that Nekrasov\\\'s partition function satisfies W-geometry constraints. %B Phys. Lett. B 691 (2010) 111-115 %G en_US %U http://hdl.handle.net/1963/3831 %1 496 %2 Physics %3 Elementary Particle Theory %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-01-26T15:40:23Z\\nNo. of bitstreams: 1\\n0909.4031.pdf: 120604 bytes, checksum: 7f2242b71035ba7cad650ea81a13d801 (MD5) %R 10.1016/j.physletb.2010.06.027 %0 Report %D 2010 %T Moore-Read Fractional Quantum Hall wavefunctions and SU(2) quiver gauge theories %A Raoul Santachiara %A Alessandro Tanzini %X We identify Moore-Read wavefunctions, describing non-abelian statistics in fractional quantum Hall systems, with the instanton partition of N=2 superconformal quiver gauge theories at suitable values of masses and \\\\Omega-background parameters. This is obtained by extending to rational conformal field theories the SU(2) gauge quiver/Liouville field theory duality recently found by Alday-Gaiotto-Tachikawa. A direct link between the Moore-Read Hall $n$-body wavefunctions and Z_n-equivariant Donaldson polynomials is pointed out. %G en_US %U http://hdl.handle.net/1963/3852 %1 857 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-03-02T08:00:48Z\\nNo. of bitstreams: 1\\n14_2010_FM.pdf: 390526 bytes, checksum: 871ac8b351d4f1610b0120a9e7a5201a (MD5) %0 Journal Article %J JHEP 06(2010)063 %D 2010 %T Taming open/closed string duality with a Losev trick %A Giulio Bonelli %A Andrea Prudenziati %A Alessandro Tanzini %X A target space string field theory formulation for open and closed B-model is provided by giving a Batalin-Vilkovisky quantization of the holomorphic Chern-Simons theory with off-shell gravity background. The target space expression for the coefficients of the holomorphic anomaly equation for open strings are obtained. Furthermore, open/closed string duality is proved from a judicious integration over the open string fields. In particular, by restriction to the case of independence on continuous open moduli, the shift formulas of [7] are reproduced and shown therefore to encode the data of a closed string dual. %B JHEP 06(2010)063 %G en_US %U http://hdl.handle.net/1963/3855 %1 854 %2 Physics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-04-27T10:19:29Z\\nNo. of bitstreams: 1\\nBonelli_1003.2519v2.pdf: 244116 bytes, checksum: e9e48e420eda839f478ab8a4da3e7136 (MD5) %R 10.1007/JHEP06(2010)063 %0 Journal Article %J JHEP 06 (2009) 046 %D 2009 %T Decoupling A and B model in open string theory: topological adventures in the world of tadpoles %A Giulio Bonelli %A Andrea Prudenziati %A Alessandro Tanzini %A Yang Jie %X In this paper we analyze the problem of tadpole cancellation in open topological strings. We prove that the inclusion of unorientable worldsheet diagrams guarantees a consistent decoupling of A and B model for open superstring amplitudes at all genera. This is proven by direct microscopic computation in Super Conformal Field Theory. For the B-model we explicitly calculate one loop amplitudes in terms of analytic Ray-Singer torsions of appropriate vector bundles and obtain that the decoupling corresponds to the cancellation of D-brane and orientifold charges. Local tadpole cancellation on the worldsheet then guarantees the decoupling at all loops. The holomorphic anomaly equations for open topological strings at one loop are also obtained and compared with the results of the Quillen formula. %B JHEP 06 (2009) 046 %G en_US %U http://hdl.handle.net/1963/3632 %1 672 %2 Physics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-05-14T12:10:45Z\\nNo. of bitstreams: 1\\n0905.1286v1.pdf: 335944 bytes, checksum: fe5d3723cd904f1c7123c5bc83356013 (MD5) %R 10.1088/1126-6708/2009/06/046 %0 Journal Article %J Comm. Math. Phys. 289 (2009) 205-252 %D 2009 %T Exact results for topological strings on resolved Yp,q singularities %A Andrea Brini %A Alessandro Tanzini %B Comm. Math. Phys. 289 (2009) 205-252 %G en_US %U http://hdl.handle.net/1963/2631 %1 1492 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-04-16T11:13:40Z\\nNo. of bitstreams: 1\\npicard-b.pdf: 387933 bytes, checksum: 2261a0d091c9829eb1d1b55b77b1a42e (MD5) %R 10.1007/s00220-009-0814-4 %0 Journal Article %J Phys. Lett. B 672 (2009) 390-395 %D 2009 %T Topological branes, p-algebras and generalized Nahm equations %A Giulio Bonelli %A Alessandro Tanzini %A Maxim Zabzine %X Inspired by the recent advances in multiple M2-brane theory, we consider the generalizations of Nahm equations for arbitrary p-algebras. We construct the topological p-algebra quantum mechanics associated to them and we show that this can be obtained as a truncation of the topological p-brane theory previously studied by the authors. The resulting topological p-algebra quantum mechanics is discussed in detail and the relation with the M2-M5 system is pointed out in the p=3 case, providing a geometrical argument for the emergence of the 3-algebra structure in the Bagger-Lambert-Gustavsson theory %B Phys. Lett. B 672 (2009) 390-395 %G en_US %U http://hdl.handle.net/1963/2702 %1 1398 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-08-08T15:57:12Z\\nNo. of bitstreams: 1\\n0807.5113v1.pdf: 246583 bytes, checksum: 0013b3623fd81d20db0fb541bd4b9dd4 (MD5) %R 10.1016/j.physletb.2009.01.051 %0 Report %D 2008 %T Instanton counting on Hirzebruch surfaces %A Ugo Bruzzo %A Rubik Poghossian %A Alessandro Tanzini %X We perform a study of the moduli space of framed torsion free sheaves on Hirzebruch surfaces by using localization techniques. After discussing general properties of this moduli space, we classify its fixed points under the appropriate toric action and compute its Poincare\\\' polynomial. From the physical viewpoint, our results provide the partition function of N=4 Vafa-Witten theory on Hirzebruch surfaces, which is relevant in black hole entropy counting problems according to a conjecture due to Ooguri, Strominger and Vafa. %G en_US %U http://hdl.handle.net/1963/2852 %1 1848 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-05T18:06:43Z\\nNo. of bitstreams: 1\\n0809.0155v1.pdf: 212427 bytes, checksum: f5060bd4e1da6a5215a488041ef018ff (MD5) %0 Journal Article %J Adv. Theor. Math. Phys. 12 (2008) 1429-1446 %D 2008 %T Topological Gauge Theories on Local Spaces and Black Hole Entropy Countings %A Giulio Bonelli %A Alessandro Tanzini %X We study cohomological gauge theories on total spaces of holomorphic line bundles over complex manifolds and obtain their reduction to the base manifold by U(1) equivariant localization of the path integral. We exemplify this general mechanism by proving via exact path integral localization a reduction for local curves conjectured in hep-th/0411280, relevant to the calculation of black hole entropy/Gromov-Witten invariants. Agreement with the four-dimensional gauge theory is recovered by taking into account in the latter non-trivial contributions coming from one-loop fluctuations determinants at the boundary of the total space. We also study a class of abelian gauge theories on Calabi-Yau local surfaces, describing the quantum foam for the A-model, relevant to the calculation of Donaldson-Thomas invariants. %B Adv. Theor. Math. Phys. 12 (2008) 1429-1446 %G en_US %U http://hdl.handle.net/1963/1992 %1 2204 %2 Physics %3 Elementary Particle Theory %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-08-09T12:45:15Z\\nNo. of bitstreams: 1\\nhep-th0706.2633v1.pdf: 170115 bytes, checksum: 16cdd3d36705e91d5d429948e55b15a5 (MD5) %0 Report %D 2007 %T Black Holes, Instanton Counting on Toric Singularities and q-Deformed Two-Dimensional Yang-Mills Theory %A Luca Griguolo %A Domenico Seminara %A Richard J. Szabo %A Alessandro Tanzini %X We study the relationship between instanton counting in N=4 Yang-Mills theory on a generic four-dimensional toric orbifold and the semi-classical expansion of q-deformed Yang-Mills theory on the blowups of the minimal resolution of the orbifold singularity, with an eye to clarifying the recent proposal of using two-dimensional gauge theories to count microstates of black holes in four dimensions. We describe explicitly the instanton contributions to the counting of D-brane bound states which are captured by the two-dimensional gauge theory. We derive an intimate relationship between the two-dimensional Yang-Mills theory and Chern-Simons theory on generic Lens spaces, and use it to show that the correct instanton counting is only reproduced when the Chern-Simons contributions are treated as non-dynamical boundary conditions in the D4-brane gauge theory. We also use this correspondence to discuss the counting of instantons on higher genus ruled Riemann surfaces. %B Nucl. Phys. B 772 (2007) 1-24 %G en_US %U http://hdl.handle.net/1963/1888 %1 2347 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-11-09T10:57:35Z\\nNo. of bitstreams: 1\\nhep-th0610155.pdf: 340757 bytes, checksum: fb3e5bfec5e2a4c15d97a9ca6f2e8a0a (MD5) %R 10.1016/j.nuclphysb.2007.02.030 %0 Report %D 2007 %T The complete one-loop spin chain for N=2 Super-Yang-Mills %A Paolo Di Vecchia %A Alessandro Tanzini %X We show that the complete planar one-loop mixing matrix of the N=2 Super Yang--Mills theory can be obtained from a reduction of that of the N=4 theory. For composite operators of scalar fields, this yields an anisotropic XXZ spin chain, whose spectrum of excitations displays a mass gap. %G en_US %U http://hdl.handle.net/1963/2309 %1 1707 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-29T14:28:13Z\\nNo. of bitstreams: 1\\n0412283v1.pdf: 110673 bytes, checksum: 9f881078e3eb69765e2c6e294569fd70 (MD5) %0 Report %D 2007 %T Computing Amplitudes in topological M-theory %A Giulio Bonelli %A Alessandro Tanzini %A Maxim Zabzine %X We define a topological quantum membrane theory on a seven dimensional manifold of $G_2$ holonomy. We describe in detail the path integral evaluation for membrane geometries given by circle bundles over Riemann surfaces. We show that when the target space is $CY_3\\\\times S^1$ quantum amplitudes of non-local observables of membranes wrapping the circle reduce to the A-model amplitudes. \\nIn particular for genus zero we show that our model computes the Gopakumar-Vafa invariants. Moreover, for membranes wrapping calibrated homology spheres in the $CY_3$, we find that the amplitudes of our model are related to Joyce invariants. %B JHEP 03 (2007) 023 %G en_US %U http://hdl.handle.net/1963/1901 %1 2335 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-12-07T16:26:28Z\\nNo. of bitstreams: 1\\nhep-th0611327.pdf: 307312 bytes, checksum: 9a3a9891aca40624a44c7a531765695b (MD5) %R 10.1088/1126-6708/2007/03/023 %0 Journal Article %J JHEP 10 (2007) 060 %D 2007 %T The holomorphic anomaly for open string moduli %A Giulio Bonelli %A Alessandro Tanzini %X We complete the holomorphic anomaly equations for topological strings with their dependence on open moduli. We obtain the complete system by standard path integral arguments generalizing the analysis of BCOV (Commun. Math. Phys. 165 (1994) 311) to strings with boundaries. We study both the anti-holomorphic dependence on open moduli and on closed moduli in presence of Wilson lines. By providing the compactification a\\\' la Deligne-Mumford of the moduli space of Riemann surfaces with boundaries, we show that the open holomorphic anomaly equations are structured on the (real codimension one) boundary components of this space. %B JHEP 10 (2007) 060 %G en_US %U http://hdl.handle.net/1963/2113 %1 2576 %2 Physics %3 Elementary Particle Theory %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-17T09:24:42Z\\nNo. of bitstreams: 1\\n0708.2627v2.pdf: 199897 bytes, checksum: 38929fe4fa52ddd01dd4af02292f3058 (MD5) %R 10.1088/1126-6708/2007/10/060 %0 Report %D 2006 %T N=1 superpotentials from multi-instanton calculus %A Francesco Fucito %A Jose F. Morales %A Rubik Poghossian %A Alessandro Tanzini %X In this paper we compute gaugino and scalar condensates in N = 1 supersymmetric gauge\\ntheories with and without massive adjoint matter, using localization formulae over the multi-instanton moduli space. Furthermore we compute the chiral ring relations among the correlators of the N = 1* theory and check this result against the multi-instanton computation finding agreement. %B JHEP01(2006)031 %G en_US %U http://hdl.handle.net/1963/1773 %1 2771 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-03-29T07:58:23Z\\nNo. of bitstreams: 1\\n73FM-2005.pdf: 325303 bytes, checksum: 89f205e907378d543e7a51042f437c8a (MD5) %R 10.1088/1126-6708/2006/01/031 %0 Report %D 2006 %T On topological M-theory %A Giulio Bonelli %A Alessandro Tanzini %A Maxim Zabzine %X We construct a gauge fixed action for topological membranes on G2-manifolds such that its bosonic part is the standard membrane theory in a particular gauge. We prove that quantum mechanically the path-integral in this gauge localizes on associative submanifolds. %B Adv. Theor. Math. Phys. 10 (2006) 239-260 %G en_US %U http://hdl.handle.net/1963/1765 %1 2779 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-03-23T14:41:22Z\\nNo. of bitstreams: 1\\n64FM.pdf: 240192 bytes, checksum: 3c2a8717b7a8a0d235cc7a6ef9e76369 (MD5) %0 Journal Article %J J. Geom. Phys. 56 (2006) 2379-2401 %D 2006 %T Topological symmetry of forms, N=1 supersymmetry and S-duality on special manifolds %A Laurent Baulieu %A Alessandro Tanzini %X We study the quantization of a holomorphic two-form coupled to a Yang-Mills field on special manifolds in various dimensions, and we show that it yields twisted supersymmetric theories. The construction determines ATQFT\\\'s (Almost Topological Quantum Field Theories), that is, theories with observables that are invariant under changes of metrics belonging to restricted classes. For Kahler manifolds in four dimensions, our topological model is related to N=1 Super Yang-Mills theory. Extended supersymmetries are recovered by considering the coupling with chiral multiplets. We also analyse Calabi-Yau manifolds in six and eight dimensions, and seven dimensional G_2 manifolds of the kind recently discussed by Hitchin. We argue that the two-form field could play an interesting role for the study of the conjectured S-duality in topological string. We finally show that in the case of real forms in six dimensions the partition function of our topological model is related to the square of that of the holomorphic Chern-Simons theory, and we discuss the uplift to seven dimensions and its relation with the recent proposals for the topological M-theory. %B J. Geom. Phys. 56 (2006) 2379-2401 %G en_US %U http://hdl.handle.net/1963/2168 %1 2076 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-03T07:58:25Z\\nNo. of bitstreams: 1\\n0412014v2.pdf: 317935 bytes, checksum: a9478cff2fa4dc504efece63810fb6ed (MD5) %R 10.1016/j.geomphys.2005.12.006 %0 Report %D 2005 %T Topological vector symmetry, topological gauge fixing of BRSTQFT and construction of maximal supersymmetry %A Laurent Baulieu %A Guillaume Bossard %A Alessandro Tanzini %X The scalar and vector topological Yang-Mills symmetries determine a closed and consistent sector of Yang-Mills supersymmetry. We provide a geometrical construction of these symmetries, based on a horizontality condition on reducible manifolds. This yields globally well-defined scalar and vector topological BRST operators. These operators generate a subalgebra of maximally supersymmetric Yang-Mills theory, which is small enough to be closed off-shell with a finite set of auxiliary fields and large enough to determine the Yang-Mills supersymmetric theory. Poincaré supersymmetry is reached in the limit of flat manifolds. The arbitrariness of the gauge functions in BRSTQFTs is thus removed by the requirement of scalar and vector topological symmetry, which also determines the complete supersymmetry transformations in a twisted way. Provided additional Killing vectors exist on the manifold, an equivariant extension of our geometrical framework is provided, and the resulting \\\"equivariant topological field theory\\\" corresponds to the twist of super Yang-Mills theory on omega backgrounds. %B JHEP 0508 (2005) 037 %G en_US %U http://hdl.handle.net/1963/1741 %1 2411 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-02-23T10:07:01Z\\nNo. of bitstreams: 1\\nhep-th0504224.pdf: 434040 bytes, checksum: 925f48080ebdefb366d603cd196cba76 (MD5) %R 10.1088/1126-6708/2005/08/037 %0 Journal Article %J J.High Energy Phys. 2003,no.5,054,24 pp. %D 2003 %T Multi-instanton calculus and equivariant cohomology %A Ugo Bruzzo %A Jose F. Morales %A Francesco Fucito %A Alessandro Tanzini %B J.High Energy Phys. 2003,no.5,054,24 pp. %I SISSA Library %G en %U http://hdl.handle.net/1963/1645 %1 2473 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T13:05:48Z (GMT). No. of bitstreams: 1\\nhep-th0211108.pdf: 318316 bytes, checksum: 6253a1679129f66f68bcd94e85931a56 (MD5)\\n Previous issue date: 2002 %R 10.1088/1126-6708/2003/05/054 %0 Journal Article %J Nuclear Phys. B 611 (2001), no. 1-3, 205--226. %D 2001 %T On the Multi-Instanton Measure for Super Yang-Mills Theories %A Ugo Bruzzo %A Francesco Fucito %A Alessandro Tanzini %A Gabriele Travaglini %B Nuclear Phys. B 611 (2001), no. 1-3, 205--226. %I SISSA Library %G en %U http://hdl.handle.net/1963/1531 %1 2632 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T13:03:42Z (GMT). No. of bitstreams: 1\\nhep-th0008225.pdf: 293471 bytes, checksum: 20088b444ac5b59f0f868d44e40731cc (MD5)\\n Previous issue date: 2000 %R 10.1016/S0550-3213(01)00349-2