%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
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%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
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%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
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%R 10.1007/s00220-014-2193-8