Partial Ordering of Gauge Orbit Types for SU(n)-Gauge Theories

TL;DR

This paper investigates the partial ordering of gauge orbit types in SU(n)-gauge theories, using cohomology to characterize the relations and providing algebraic methods to generate and reconstruct orbit types.

Contribution

It introduces an algebraic characterization of the partial ordering of gauge orbit types via cohomology elements, enabling systematic reconstruction of orbit types.

Findings

Partial ordering characterized by algebraic equations

Operations to generate direct successors and predecessors

Reconstruction of orbit types from principal type

Abstract

The natural partial ordering of the orbit types of the action of the group of local gauge transformations on the space of connections in space-time dimension d<=4 is investigated. For that purpose, a description of orbit types in terms of cohomology elements of space-time, derived earlier, is used. It is shown that, on the level of these cohomology elements, the partial ordering relation is characterized by a system of algebraic equations. Moreover, operations to generate direct successors and direct predecessors are formulated. The latter allow to successively reconstruct the set of orbit types, starting from the principal type.