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 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.)
Moore, G;
[1]
Nekrasov, N;
[2]
Shatashvili, S
[3]
- Yale Univ., New Haven, CT (United States). Dept. of Physics
- Institute of Theoretical and Experimental Physics, 117259, Moscow (Russian Federation)
- Lyman Laboratory of Physics, Harvard University, Cambridge, MA (United States)
Citation Formats
Moore, G, Nekrasov, N, and Shatashvili, S.
Integrating over Higgs branches.
Germany: N. p.,
2000.
Web.
doi:10.1007/PL00005525.
Moore, G, Nekrasov, N, & Shatashvili, S.
Integrating over Higgs branches.
Germany.
https://doi.org/10.1007/PL00005525
Moore, G, Nekrasov, N, and Shatashvili, S.
2000.
"Integrating over Higgs branches."
Germany.
https://doi.org/10.1007/PL00005525.
@misc{etde_20097313,
title = {Integrating over Higgs branches}
author = {Moore, G, Nekrasov, N, and Shatashvili, S}
abstractNote = {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.)}
doi = {10.1007/PL00005525}
journal = []
issue = {1}
volume = {209}
journal type = {AC}
place = {Germany}
year = {2000}
month = {Jan}
}
title = {Integrating over Higgs branches}
author = {Moore, G, Nekrasov, N, and Shatashvili, S}
abstractNote = {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.)}
doi = {10.1007/PL00005525}
journal = []
issue = {1}
volume = {209}
journal type = {AC}
place = {Germany}
year = {2000}
month = {Jan}
}