Subleading Correction to Statistical Entropy for BMPV Black Hole

TL;DR

The paper develops a method to compute subleading, higher-derivative corrections to the statistical entropy of five-dimensional BMPV black holes by leveraging a degeneracy function constructed from the four-dimensional dyonic black holes. It formulates the BMPV degeneracy via a modified modular function tildePhi_bmpv and uses a v-residue based analysis to obtain the O(Q^0) correction to the statistical entropy through a one-loop effective action, validating results against exact degeneracies for large charges. The approach generalizes to CHL-like 5D black holes, preserving the same qualitative behavior, and highlights a key distinction from 4D: no walls of marginal stability affect the BMPV degeneracy, making the non-Cardy regime accessible. Overall, the work demonstrates that the statistical entropy function can yield systematic, higher-derivative corrections beyond the Cardy limit for 5D black holes.

Abstract

We study higher derivative corrections to the statistical entropy function and the statistical entropy for five dimensional BMPV black holes by doing the asymptotic expansion of the partition function. This enables us to evaluate entropy for a large range of charges, even out of Cardy (Farey tail) limit.