Non-supersymmetric black holes with $\alpha'$ corrections

TL;DR

This paper analyzes how $oldsymbol{ ext{α'}}}$ corrections affect extremal black holes in heterotic string theory, revealing significant differences between supersymmetric and non-supersymmetric cases and confirming the Weak Gravity Conjecture.

Contribution

It provides the first fully analytic $oldsymbol{ ext{α'}}}$-corrected solutions for extremal black holes with arbitrary charges and signs, including non-supersymmetric cases, and extends entropy formulas.

Findings

$oldsymbol{ ext{α'}}}$ corrections vary drastically with supersymmetry breaking.

Mass shifts due to $oldsymbol{ ext{α'}}}$ corrections are always negative.

Corrected entropy formula generalizes previous results.

Abstract

We study extremal 5- and 4-dimensional black hole solutions of the Heterotic Superstring effective action at first order in $\alpha'$ with, respectively, 3 and 4 charges of arbitrary signs. For a particular choice of the relative signs of these charges the solutions are supersymmetric, but other signs give rise to non-supersymmetric extremal black holes. Although at zeroth order all these solutions are formally identical, we show that the $\alpha'$ corrections are drastically different depending on how we break supersymmetry. We provide fully analytic $\mathcal{O}(\alpha')$ solutions and we compute their charges, masses and entropies and check that they are invariant under $\alpha'$-corrected T-duality transformations. The masses of some of these black holes are corrected in a complicated way, but we show that the shift is always negative, in agreement with the Weak Gravity Conjecture. Our formula for the corrected entropy of the four-dimensional black holes generalizes previous results obtained from the entropy function method, as we consider a more general way in which supersymmetry can be broken.