# Exact charges from heterotic black holes

## TL;DR

This paper derives exact charge relations for heterotic black holes incorporating all orders of string corrections, confirming their consistency with microscopic entropy calculations and analyzing the impact of higher-curvature terms.

## Contribution

It provides exact formulas for heterotic black hole charges including all string corrections, extending previous quadratic-order approximations and clarifying the role of higher-curvature terms.

## Key findings

- Exact charge relations match microscopic entropy calculations.
- Higher-curvature corrections cause a shift between near-horizon and asymptotic charges.
- Gauss-Bonnet term reproduces Wald entropy in some cases but not all.

## Abstract

We derive exact relations to all orders in the $\alpha'$ expansion for the charges of a bound system of heterotic strings, solitonic 5-branes and, optionally, a Kaluza-Klein monopole. The expressions, which differ from those of the zeroth-order supergravity approximation, coincide with the values obtained when only the corrections of quadratic order in curvature are included. Our computation relies on the consistency of string theory as a quantum theory of gravity; the relations follow from the matching of the Wald entropy with the microscopic degeneracy. In the heterotic frame, the higher-curvature terms behave as delocalized sources that introduce a shift between near-horizon and asymptotic charges. On the other hand, when described in terms of lower-dimensional effective fields, the solution carries constant charges over space which coincide with those of the asymptotic heterotic fields. In addition, we describe why the Gauss-Bonnet term, which only captures a subset of the relevant corrections of quadratic order in curvature, in some cases succeeds to reproduce the correct value for the Wald entropy, while fails in others.