Classification of Gauge Orbit Types for SU(n)-Gauge Theories
Abstract
A method for determining the orbit types of the action of the group of gauge transformations on the space of connections for gauge theories with gauge group SU(n) in space-time dimension d<=4 is presented. The method is based on the 1:1-correspondence between orbit types and holonomy-induced Howe subbundles of the underlying principal SU(n)-bundle. It is shown that the orbit types are labelled by certain cohomology elements of space-time satisfying two relations. Thus, for every principal SU(n)-bundle the corresponding stratification of the gauge orbit space can be determined explicitly. As an application, a criterion characterizing kinematical nodes for physical states in 2+1-dimensional Chern-Simons theory proposed by Asorey et al. is discussed.
Cite
@article{arxiv.math-ph/0003044,
title = {Classification of Gauge Orbit Types for SU(n)-Gauge Theories},
author = {Gerd Rudolph and Matthias Schmidt and Igor P. Volobuev},
journal= {arXiv preprint arXiv:math-ph/0003044},
year = {2009}
}
Comments
47 pages, LaTeX; revised version