Quantum integrability and supersymmetric vacua

Abstract

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

21 pp., short version II, conference in honour of T.Eguchi's 60th anniversary; v2. typos and refs corrected

References in corpus (3)

• Supersymmetric vacua and Bethe ansatz
• Higgs Bundles, Gauge Theories and Quantum Groups
• Analytic theory of the eight-vertex model

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