Integrating Over Higgs Branches
摘要
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.
引用
@article{arxiv.hep-th/9712241,
title = {Integrating Over Higgs Branches},
author = {G. Moore and N. Nekrasov and S. Shatashvili},
journal= {arXiv preprint arXiv:hep-th/9712241},
year = {2009}
}
备注
32pp. harvmac big mode; v.2 34pp. typos fixed, sections 4.1, 5.2 substantially improved