Covariant Noether Charge for Higher Dimensional Chern-Simons Terms

TL;DR

This paper develops a covariant differential Noether charge framework for higher-dimensional theories with Chern-Simons terms, enabling a covariant derivation of entropy formulas related to black hole thermodynamics.

Contribution

It introduces a covariant construction of the differential Noether charge for higher-dimensional Chern-Simons theories, improving upon previous non-covariant approaches.

Findings

The covariant charge integrates to Tachikawa's Wald-like entropy formula.

The formalism maintains covariance unlike previous methods.

Application to higher-dimensional black hole entropy calculations.

Abstract

We construct a manifestly covariant differential Noether charge for theories with Chern-Simons terms in higher dimensional spacetimes. This is in contrast to Tachikawa's extension of the standard Lee-Iyer-Wald formalism which results in a non-covariant differential Noether charge for Chern-Simons terms. On a bifurcation surface, our differential Noether charge integrates to the Wald-like entropy formula proposed by Tachikawa in arXiv:hep-th/0611141.