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Classification of Gauge Orbit Types for SU(n)-Gauge Theories

Gerd Rudolph·Matthias Schmidt·Igor P. Volobuev
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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.

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Gerd Rudolph, Matthias Schmidt, Igor P. Volobuev. 2000-04-10. Classification of Gauge Orbit Types for SU(n)-Gauge Theories. https://arxiv.org/abs/math-ph/0003044

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