Transgression forms and extensions of Chern-Simons gauge theories

TL;DR

This paper introduces a gauge invariant action principle using transgression forms, extending Chern-Simons theories by adding boundary terms to ensure gauge invariance and regularize black hole solutions in gravitational contexts.

Contribution

It proposes a new gauge invariant action based on transgression forms that extends Chern-Simons theories and improves the treatment of black hole geometries.

Findings

The action is gauge invariant and finite for black hole solutions.

Black hole thermodynamics is accurately reproduced.

Energy calculations agree with Noether's theorem.

Abstract

A gauge invariant action principle, based on the idea of transgression forms, is proposed. The action extends the Chern-Simons form by the addition of a boundary term that makes the action gauge invariant (and not just quasi-invariant). Interpreting the spacetime manifold as cobordant to another one, the duplication of gauge fields in spacetime is avoided. The advantages of this approach are particularly noticeable for the gravitation theory described by a Chern-Simons lagrangian for the AdS group, in which case the action is regularized and finite for black hole geometries in diverse situations. Black hole thermodynamics is correctly reproduced using either a background field approach or a background-independent setting, even in cases with asymptotically nontrivial topologies. It is shown that the energy found from the thermodynamic analysis agrees with the surface integral obtained by direct application of Noether's theorem.