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arXiv · hep-th/9712241

Integrating Over Higgs Branches

G. Moore·N. Nekrasov·S. Shatashvili
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Abstract

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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G. Moore, N. Nekrasov, S. Shatashvili. 2006-12-12. Integrating Over Higgs Branches. https://doi.org/10.1007/pl00005525

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