T duality and Wald entropy formula in the Heterotic Superstring effective action at first order in $\alpha'$

TL;DR

This paper investigates T duality and Wald entropy in the first-order $mbda'$-corrected heterotic superstring effective action, deriving corrected Buscher rules, proving T duality invariance, and applying an entropy formula to black hole solutions.

Contribution

It derives $mbda'$-corrected Buscher rules, proves T duality invariance of the reduced action, and extends Wald entropy application to heterotic black holes at first order in $mbda'$.

Findings

Confirmed T duality invariance of the $mbda'$-corrected action.

Derived an entropy formula applicable to heterotic black holes.

Applied the entropy formula to a heterotic Strominger-Vafa black hole.

Abstract

We consider the compactification on a circle of the Heterotic Superstring effective action to first order in the Regge slope parameter $\alpha'$ and re-derive the $\alpha'$-corrected Buscher rules first found in arXiv:hep-th/9506156 , proving the T duality invariance of the dimensionally-reduced action to that order in $\alpha'$. We use Iyer and Wald's prescription to derive an entropy formula that can be applied to black-hole solutions which can be obtained by a single non-trivial compactification on a circle and discuss its invariance under the $\alpha'$-corrected T duality transformations. This formula has been successfully applied to $\alpha'$-corrected 4-dimensional non-extremal Reissner-Nordstr\"om black holes in arXiv:1910.14324 and we apply it here to a heterotic version of the Strominger-Vafa 5-dimensional extremal black hole.