01519nas 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/1963/34546