01192nas a2200181   4500008004100000022001400041245008800055210006900143260000800212300000700220490000900227520063800236100002200874700002000896700002600916700002400942856004400966       2016                        eng d  a1029-847900aSymmetry enhancements via 5d instantons, qW-algebrae and (1,0) superconformal index0 aSymmetry enhancements via 5d instantons qWalgebrae and 10 superc  cSep  a530 v20163 a<p>We 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.</p>1 aBenvenuti, Sergio1 aBonelli, Giulio1 aRonzani, Massimiliano1 aTanzini, Alessandro  uhttps://doi.org/10.1007/JHEP09(2016)05301519nas a2200145   4500008004100000245015300041210006900194260001300263520096300276100002001239700002301259700002401282700001601306856005101322       2014                        en  d00aSix-dimensional supersymmetric gauge theories, quantum cohomology of instanton moduli spaces and gl(N) Quantum Intermediate Long Wave  Hydrodynamics0 aSixdimensional supersymmetric gauge theories quantum cohomology   bSpringer3 aWe 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.1 aBonelli, Giulio1 aSciarappa, Antonio1 aTanzini, Alessandro1 aVasko, Petr  uhttp://urania.sissa.it/xmlui/handle/1963/3454601412nas a2200145   4500008004100000245004500041210004100086260001300127520099200140100002001132700002301152700002401175700001601199856005101215       2014                        en  d00aThe stringy instanton partition function0 astringy instanton partition function  bSpringer3 aWe 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^2.1 aBonelli, Giulio1 aSciarappa, Antonio1 aTanzini, Alessandro1 aVasko, Petr  uhttp://urania.sissa.it/xmlui/handle/1963/34589