Non standard parametrizations and adjoint invariants of classical groups

TL;DR

This paper develops local parametrizations of classical non-compact Lie groups that clearly display adjoint invariants, with applications to gauge theories and string theory models.

Contribution

It introduces new local parametrizations of classical non-compact Lie groups highlighting adjoint invariants, useful for gauge-invariant theories and string backgrounds.

Findings

Parametrizations explicitly show adjoint invariants.

Extension to non-compact subgroups is straightforward.

Applications to gauged Wess-Zumino-Witten-Novikov models.

Abstract

We obtain local parametrizations of classical non-compact Lie groups where adjoint invariants under maximal compact subgroups are manifest. Extension to non compact subgroups is straightforward. As a by-product parametrizations of the same type are obtained for compact groups. They are of physical interest in any theory gauge invariant under the adjoint action, typical examples being the two dimensional gauged Wess-Zumino-Witten-Novikov models where these coordinatizations become of extreme usefulness to get the background fields representing the vacuum expectation values of the massless modes of the associated (super) string theory.