Non-supersymmetric black holes with α′ corrections
Pablo A. Cano, Tomás Ortı́n, Alejandro Ruipérez, Matteo Zatti
Abstract
A bstract We study extremal 5- and 4-dimensional black hole solutions of the Heterotic Superstring effective action at first order in α′ 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 α ′ corrections are drastically different depending on how we break supersymmetry. We provide fully analytic $$ \mathcal{O} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>O</mml:mi></mml:math> ( α ′) solutions and we compute their charges, masses and entropies and check that they are invariant under α ′-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.