LisMath Seminar 

21/04/2022, 15:00 — 15:30 — Online
Martí Rosselló, Instituto Superior Técnico, Universidade de Lisboa

Rademacher Expansion of a Siegel Modular Form and Black Hole Entropy

The degeneracies of 1/4 BPS states with unit torsion in heterotic string theory compactified on a six-torus are given in terms of the Fourier coefficients of the reciprocal of the Igusa cusp Siegel modular form $\Phi_{10}$ of weight 10. We use the symplectic symmetries of the latter to construct a fine-grained Rademacher type expansion which expresses these BPS degeneracies as a regularized sum over residues of the poles of $1/\Phi_{10}$. This construction shows how the polar data of a family of mock Jacobi forms are explicitly built from the Fourier coefficients of $1/\eta^{24}$ by means of a continued fraction structure, confirming previous results and providing a guide for the computation of the exact quantum entropy of $1/4$ BPS black holes in four-dimensional supergravity.