Non-supersymmetric black holes with ${\alpha }^{\prime }$ corrections

Abstract

We study extremal 5- and 4-dimensional black hole solutions of the Heterotic Superstring effective action at first order in ${\alpha }^{\prime }$ 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 ${\alpha }^{\prime }$ corrections are drastically different depending on how we break supersymmetry. We provide fully analytic $\mathcal{O}({\alpha }^{\prime })$ solutions and we compute their charges, masses and entropies and check that they are invariant under ${\alpha }^{\prime }$-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.

arXiv comment58 pages, 1 figure, version to be sent to JHEP (improved presentation and typos fixed)

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