%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