Transgression forms and extensions of Chern-Simons gauge theories

TL;DR

The paper develops a gauge-invariant action principle for gravity via transgression forms, introducing two CS connections $A$ and $\bar{A}$ living on cobordant manifolds and interacting only at a common boundary. This yields a background-independent, finite action with well-defined conserved charges and reproduces black hole thermodynamics consistently in Euclidean and Noether frameworks, even for topologically nontrivial horizons. By recasting CS gravity as a transgression form for the AdS group, the authors obtain gauge-invariant boundary terms that regularize the action and align thermodynamic energy with Noether charges, providing a robust, dual-view approach to AdS gravity and its holographic implications.

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.