Supersymmetric vacua and Bethe ansatz

Abstract

This note is a short announcement of some results of a longer p aper where the supersymmet- ric vacua of two dimensional N = 4 gauge theories with matter, softly broken by the twisted masses down to N = 2, are shown to be in one-to-one correspondence with the eig enstates of integrable spin chain Hamiltonians. The Heisenberg SU (2) XXX 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 theor y compactified on a circle, the XY Z spin chain and eight-vertex model are related to the four dim ensional theory compactified on T 2 . The correspondence extends to any spin group, representati ons, boundary conditions, and inho- mogeneity, it includes Sinh-Gordon and non-linear Schr ?od inger models as well as the dynamical spin chains such as the Hubbard model. Compactifications of f our dimensional N = 2 theories on a two-sphere lead to the instanton-corrected Bethe equat ions. We propose a completely novel way for the Yangian, quantum affine, and elliptic algebras to a ct as a symmetry of a union of quantum field theories