Black hole entropy, quantum corrections and EFT transitions

A bstract We revisit and study quantum corrections to the supersymmetric entropy of BPS black holes in 4d $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 2 effective field theories (EFTs), which can be obtained from Type IIA string theory compactified on a Calabi-Yau threefold. Macroscopically, these corrections arise from an infinite series of higher-derivative F-terms that encode certain modifications to the two-derivative supergravity effective action. Within the large volume regime, we analyze in detail the moduli dependence of these semi-classical contributions and explore their implications for the black hole entropy. As a byproduct, we show that the latter captures, in a rather intricate way, the transition between four- and five-dimensional dual EFT descriptions. In fact, the expansion parameter α controlling the relevant asymptotic series can be related to the ratio of the black hole horizon and the Kaluza-Klein length-scale, given here by the inverse D0-brane mass. Furthermore, we are able to resum the series into a well-behaved convergent expression for all values of α . This demonstrates, in turn, that (stable) black holes can, indeed, probe scales besides the quantum gravity cutoff. More precisely, by examining two representative BPS systems — the D0-D2-D4 and D2-D6 black hole solutions — we explicitly illustrate how highly non-local yet perturbative quantum effects resolve the divergences, ultimately leading to a well-defined entropy function. Additionally, in special cases, we show that one can take a suitable decompactification limit to 5d and verify that the corrected entropy function reproduces the exact microstate counting of the underlying five-dimensional black string. Our results also clarify the role of certain non-perturbative quantum corrections, which, remarkably, do not modify any of our prior conclusions.