Quantum integrability and supersymmetric vacua

Details Quantum integrability and supersymmetric vacua Quantum integrability and supersymmetric vacua

2009-01-29

arxiv.org/abs/0901.4748v2

Prog.Theor.Phys.Suppl.177:105-119,2009

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1143/PTPS.177.105

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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