BPS invariants of N=4 gauge theory on a surface
Mathematical Physics
2013-03-19 v2 High Energy Physics - Theory
math.MP
Abstract
Generating functions of BPS invariants for N=4 U(r) gauge theory on a Hirzebruch surface with r=2 and 3 are computed. The BPS invariants provide the Betti numbers of moduli spaces of semi-stable sheaves. The generating functions for r=2 are expressed in terms of higher level Appell functions for a certain polarization of the surface. The level corresponds to the self-intersection of the base curve of the Hirzebruch surface. The non-holomorphic functions are determined, which added to the holomorphic generating functions provide functions which transform as a modular form.
Keywords
Cite
@article{arxiv.1103.0012,
title = {BPS invariants of N=4 gauge theory on a surface},
author = {Jan Manschot},
journal= {arXiv preprint arXiv:1103.0012},
year = {2013}
}
Comments
17 pages, 1 figure