Heng-Yu Chen (U. Wisc.)

A New 2d/4d Duality via Integrability

Abstract: I review various backgrounds in both four and two dimensional supersymmetric gauge theories, which lead us to conjecture a new duality between them.  Explicitly, the duality relates N=2 supersymmetric gauge theories in four dimensions to N=(2,2) gauged linear sigma-models in two dimensions. On the four dimensional side, our main example is N=2 SQCD with gauge group SU(L) and 2L fundamental flavours, whose moduli space of vacua provides a quantization of the classical Heisenberg SL(2) spin chain. Agreement with the standard quantization via the Algebraic Bethe Ansatz implies the existence of an isomorphism between the chiral ring of the 4d theory and that of a certain two-dimensional theory.  The latter can be understood as the worldvolume theory on a surface operator/vortex string probing the Higgs branch of the same 4d theory.

May 11 at 4pm in Geo/Phys Room 407