Stringy corrections to the entropy of electrically charged supersymmetric black holes with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>AdS</mml:mi></mml:mrow><mml:mrow><mml:mn>5</mml:mn></mml:mrow></mml:msub><mml:mo>×</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">S</mml:mi></mml:mrow><mml:mrow><mml:mn>5</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math> asymptotics

Abstract

We study the leading ${\ensuremath{\alpha}}^{\ensuremath{'}}$ corrections to the entropy of certain black holes with ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{S}^{5}$ asymptotics. We find that, in the supersymmetric limit, the entropy does not receive ${\ensuremath{\alpha}}^{\ensuremath{'}}$ corrections. This result strengthens recent calculations that match the index of $\mathcal{N}=4$ super-Yang-Mills with the corresponding partition function in the supersymmetric limit. In the small temperature regime, we find that the entropy corrections are concordant with the weak gravity conjecture.

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