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Integrating Over Higgs Branches

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arxiv hep-th/9712241 v2 pith:ZH6N4LV2 submitted 1997-12-28 hep-th

G.Moore , N.Nekrasov , S.Shatashvili This is my paper · ORCID
classification hep-th
keywords spaceshiggshyperkahlerquotientsvolumebrancheshitchinintegrating
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We develop some useful techinques for integrating over Higgs branches in supersymmetric theories with 4 and 8 supercharges. In particular, we define a regularized volume for hyperkahler quotients. We evaluate this volume for certain ALE and ALF spaces in terms of the hyperkahler periods. We also reduce these volumes for a large class of hyperkahler quotients to simpler integrals. These quotients include complex coadjoint orbits, instanton moduli spaces on R^4 and ALE manifolds, Hitchin spaces, and moduli spaces of parabolic Higgs bundles on Riemann surfaces. In the case of Hitchin spaces the evaluation of the volume reduces to a summation over solutions of Bethe Ansatz equations for the non-linear Schroedinger system. We discuss some applications of our results.

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Cited by 6 Pith papers

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