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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Modular forms and black holes in N=4 string theories

## Modular forms and black holes in N=4 string theoriesAdd to your list(s) Download to your calendar using vCal - Justin David (Indian Institute of Science)
- Wednesday 25 October 2023, 13:00-14:30
- Seminar Room 2, Newton Institute.
If you have a question about this talk, please contact nobody. BLH - Black holes: bridges between number theory and holographic quantum information We review the role of modular forms in counting the microscopic degeneracies of 1/4 BPS black holes in a class of N=4 string theories known as CHL models. We focus on the following 3 key aspects. For a given CHL model, the 1/4 BPS index of these states are Fourier coefficients of an inverse Siegel modular form. These Siegel modular forms are associated with the elliptic genera of K3 twisted by a Z_N automorphism, each labelled by the conjugacy classes of the Mathieu group M_24. We discuss the expansion of the inverse Siegel modular form in terms of Mock-modular forms to obtain the index of single centred black holes, and how spherical symmetry of the black hole horizon dictates the sign of this index. Finally we obtain the modular transform of the Siegel form which captures the large charge expansion of the index and its agreement with the Hawking-Bekenstein-Wald entropy. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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