Integrating over Higgs branches

Gregory Moore, Nikita Nekrasov, Samson Shatashvili

Research output: Contribution to journalArticlepeer-review

247 Scopus citations


We develop some useful techniques for integrating over Higgs branches in supersymmetric theories with 4 and 8 supercharges. In particular, we define a regularized volume for hyperkähler quotients. We evaluate this volume for certain ALE and ALF spaces in terms of the hyperkähler periods. We also reduce these volumes for a large class of hyperkähler quotients to simpler integrals. These quotients include complex coadjoint orbits, instanton moduli spaces on ℝ4 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 Schrödinger system. We discuss some applications of our results.

Original languageEnglish (US)
Pages (from-to)97-121
Number of pages25
JournalCommunications In Mathematical Physics
Issue number1
StatePublished - 2000
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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