Positivity of discrete information for CHL black holes
arXiv:2205.08726 · doi:10.1016/j.nuclphysb.2023.116095
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.
arXiv comment36 pages, many tables; v2: clarifications added, version to appear in Nuclear Physics B; v3: two typos corrected, one in the sentence after eq. (4.27) and one in the sentence after eq. (5.4), no other changes
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