Quantum integrability and supersymmetric vacua

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This is an announcement of some of the 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 correspondence between the Heisenberg spin chain and the two dimensional U(N) theory with fundamental hypermultiplets is reviewed in detail.
• We demonstrate the isomorphism of the equivariant quantum cohomology of the cotangent bundle to the Grassmanian manifold Gr(N,L) and the ring of quantum integrals of motion of the length L SU(2) XXX spin chain, in the N-particle sector.
• This paper accompanies arXiv:0901.4744