Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2009-01-29
Nucl.Phys.B, Proc.Suppl.192-193 2009:91-112,2009
Physics
High Energy Physics
High Energy Physics - Theory
35 pages, short version I, Cargese and Landau-100 conferences proceedings; v2. typos and refs corrected
Scientific paper
10.1016/j.nuclphysbps.2009.07.04
An announcement of some results of a longer paper where the supersymmetric vacua of two dimensional N=2 susy gauge theories with matter are shown to be in one-to-one correspondence with the eigenstates of integrable spin chain Hamiltonians. The Heisenberg spin chain is mapped to the two dimensional U(N) theory with fundamental hypermultiplets, the XXZ spin chain is mapped to the analogous three dimensional super-Yang-Mills theory compactified on a circle, the XYZ spin chain and eight-vertex model are related to the four dimensional theory compactified on a torus. The correspondence extends to any spin group, representations, boundary conditions, and inhomogeneity, it includes Sinh-Gordon and non-linear Schroedinger models as well as the dynamical spin chains such as the Hubbard model. Compactifications of four dimensional N=2 theories on a two-sphere lead to the instanton-corrected Bethe equations. We propose a completely novel way for the Yangian, quantum affine, and elliptic algebras to act as a symmetry of a union of quantum field theories. This paper accompanies arXiv:0901.4748
Nekrasov Nikita A.
Shatashvili Samson L.
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