The first law of heterotic stringy black hole mechanics at zeroth order in alpha prime

TL;DR

This paper derives the first law of black hole mechanics within heterotic string theory at zeroth order in alpha prime, using gauge-invariant methods and Wald's formalism, setting the stage for more complex future analyses.

Contribution

It provides the first derivation of the black hole first law in heterotic string theory at leading order, handling gauge symmetries and Chern-Simons terms explicitly.

Findings

Derived the first law using gauge-invariant quantities.

Handled Abelian Chern-Simons terms and gauge symmetries.

Set groundwork for first-order alpha prime corrections.

Abstract

We re-derive the first law of black hole mechanics in the context of the Heterotic Superstring effective action compactified on a torus to leading order in alpha prime, using Wald's formalism, covariant Lie derivatives and momentum maps. The Kalb-Ramond field strength of this theory has Abelian Chern-Simons terms which induce Nicolai-Townsend transformations of the Kalb-Ramond field. We show how to deal with all these gauge symmetries deriving the first law in terms of manifestly gauge-invariant quantities. In presence of Chern-Simons terms, several definitions of the conserved charges exist, but the formalism picks up only one of them to play a role in the first law. This work is a first step towards the derivation of the first law at first order in alpha prime where, more complicated, non-Abelian, Lorentz ("gravitational") and Yang-Mills Chern-Simons terms are included in the Kalb-Ramond field strength. The derivation of a first law is a necessary step towards the derivation of a manifestly gauge-invariant entropy formula which is still lacking in the literature. In its turn, this entropy formula is needed to compare unambiguously macroscopic and microscopic black hole entropies.