The light we can see: Extracting black holes from weak Jacobi forms

TL;DR

This paper investigates how constraints on light states influence the growth of heavy states in weak Jacobi forms, revealing the robustness of leading growth and the sensitivity of subleading corrections, with applications to black hole entropy and holography.

Contribution

It introduces a method to analyze the impact of light state constraints on the asymptotic behavior of weak Jacobi forms, connecting microscopic black hole entropy to modular form properties.

Findings

Leading Cardy-like growth is robust across regimes.

Subleading corrections depend on light state constraints.

Provides new insights into black hole microstate counting.

Abstract

We quantify how constraints on light states affect the asymptotic growth of heavy states in weak Jacobi forms. The constraints we consider are sparseness conditions on the Fourier coefficients of these forms, which are necessary to interpret them as gravitational path integrals. Using crossing kernels, we extract the leading and subleading behavior of these coefficients and show that the leading Cardy-like growth is robust in a wide regime of validity. On the other hand, we find that subleading corrections are sensitive to the constraints placed on the light states, and we quantify their imprint on the asymptotic growth of states. Our approach is tested against the generating function of symmetric product orbifolds, where we provide new insights into the factors contributing to the asymptotic growth of their Fourier coefficients. Finally, we use our methods to revisit the UV/IR connection that relates black hole microstate counting to modular forms. We provide a microscopic interpretation of the logarithmic corrections to the entropy of BPS black holes in N = 2, 4 ungauged supergravity in four and five dimensions, and tie it to consistency conditions in AdS$_3$/CFT$_2$.