## Abstract

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 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 Schrödinger system. We discuss some applications of our results.

Original language | English |
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Pages (from-to) | 97-121 |

Number of pages | 25 |

Journal | Communications in Mathematical Physics |

Volume | 209 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2000 |

Externally published | Yes |