Positivity of discrete information for CHL black holes

TL;DR

This paper investigates the positivity of Fourier coefficients related to Z(N)-twined indices in CHL black holes, providing predictions and explicit tests for low charges to understand microstate charge distributions.

Contribution

It introduces a new positivity condition for Fourier coefficients of Siegel modular forms derived from black hole microstate indices and verifies these predictions for low-charge cases.

Findings

Positivity of Fourier coefficients for low charges confirmed

Predictions about charge distribution among microstates validated

Consistency checks support the theoretical framework

Abstract

Black holes carry more information about the microstates than just the total degeneracy. As a concrete example, the Z(N)-twined helicity trace indices for 1/4-BPS black holes of the CHL models allow extracting information about the distribution of the Z(N) charges among the black hole microstates. The number of black hole microstates carrying a definite eigenvalue under the generator of the Z(N) twining group must be positive. This leads to a specific prediction for the signs of certain linear combinations of Fourier coefficients of Siegel modular forms. We explicitly test these predictions for low charges. In the D1-D5-P duality frame, we compute the appropriate hair removed partition functions and show the positivity of the appropriate Fourier coefficients for low charges. We present various consistency checks on our computations.