%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