Beyond the near-horizon limit: Stringy corrections to Heterotic Black Holes

TL;DR

This paper investigates first-order stringy corrections to 4-charge heterotic black holes beyond the near-horizon limit, revealing charge shifts and entropy modifications consistent with microstate counting when higher-curvature effects are included.

Contribution

It provides a detailed analysis of $oldsymbol{ ext{α'}}$ corrections to heterotic black holes beyond the near-horizon approximation, including charge shifts and entropy calculations.

Findings

Charge shifts depend on higher-curvature corrections.

Some charge shifts can be canceled with SU(2) instantons.

Entropy matches microstate counting when corrections are included.

Abstract

We study the first-order in $\alpha'$ corrections to 4-charge black holes (with the Reissner-Nordstr\"om black hole as a particular example) beyond the near-horizon limit in the Heterotic Superstring effective action framework. The higher-curvature terms behave as delocalized sources in the equations of motion and in the Bianchi identity of the 3-form. For some charges, this introduces a shift between their values measured at the horizon and asymptotically. Some of these corrections and their associated charge shifts, but not all of them, can be canceled using appropriate SU$(2)$ instantons for the heterotic gauge fields. The entropy, computed using Wald's formula, is in agreement with the result obtained via microstate counting when the delocalized sources are properly taken into account.