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
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Dimers for Relativistic Toda Models with Reflective Boundaries
Dimer graphs are constructed for relativistic Toda chains of listed Lie algebra types, and Seiberg-Witten curves of 5d N=1 pure SYM for group G are identified as spectral curves of the dual Toda chain for G^vee.
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