Black hole entropy, quantum corrections and EFT transitions - Alberto Castellano; Matteo Zatti (Journal of High Energy Physics)
Abstract We revisit and study quantum corrections to the supersymmetric entropy of BPS black holes in 4d N $$ \mathcal{N} $$ = 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.