Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 7, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP07(2014)141
Keywords
Supersymmetric gauge theory; Solitons Monopoles and Instantons; Integrable Hierarchies; Topological Strings
Categories
Funding
- INFN Research Project GAST Nonperturbative dynamics of gauge theory
- INFN Research Project STFI
- PRIN Geometria delle varieta algebriche
- MIUR-PRIN [2009-KHZKRX]
- INFN Research Project GAST Nonperturbative dynamics of gauge theory
- INFN Research Project STFI
- PRIN Geometria delle varieta algebriche
- MIUR-PRIN [2009-KHZKRX]
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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.
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