Duality-Invariant Higher-Derivative Corrections to Charged Stringy Black Holes

We study duality-invariant higher-derivative corrections to the charged black hole geometry in two-dimensional heterotic string theory. We illustrate how the conventional perturbative approach to determine the corrected geometry breaks down. Using a non-perturbative (in $\alpha'$) parametrization of the solution, we find the corrected charge-to-mass ratio for extremal black holes. We remark on the results in relation to the weak gravity conjecture. We also consider the entropy of the extremal black hole within the attractor mechanism and find that the two-derivative entropy is not renormalized to any order. We make comments on interpretations of the results and their extension to near-extremal black holes.