Exact charges from heterotic black holes

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.