Integrating over Higgs branches Moore, G [Yale Univ., New Haven, CT (United States). Dept. of Physics]; Nekrasov, N [Institute of Theoretical and Experimental Physics, 117259, Moscow (Russian Federation)]; Shatashvili, S [Lyman Laboratory of Physics, Harvard University, Cambridge, MA (United States)] 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; HIGGS MODEL; SUPERSYMMETRY; DIFFERENTIAL GEOMETRY 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 hyperkaehler quotients. We evaluate this volume for certain ALE and ALF spaces in terms of the hyperkaehler periods. We also reduce these volumes for a large class of hyperkaehler quotients to simpler integrals. These quotients include complex coadjoint orbits, instanton moduli spaces on R{sup 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. (orig.) Germany 2000-01-01 English Journal Article Journal Name: Communications in Mathematical Physics; Journal Volume: 209; Journal Issue: 1; Other Information: 38 refs.; PBD: Jan 2000 Medium: X; Size: page(s) 97-121 https://doi.org/10.1007/PL00005525 [] 1 209 Journal ID: ISSN 0010-3616; CMPHAY; TRN: DE00FC285 DEN; EDB-00:089543 2010-12-30 20097313