Modular anomaly of BPS black holes

2024/08/29 by Sergei Alexandrov, Alexandrov, Sergei, Khalil Bendriss +1
Engineering · #Advanced Fiber Optic Sensors #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2408.16819

openalex publication_date 2024/08/29 · openalex created_date 2024/09/12 · openalex updated_date 2026/07/28

Abstract

Generating functions of BPS indices, counting states of D4-D2-D0 black holes in Calabi-Yau compactifications of type IIA string theory and identified with rank 0 Donaldson- Thomas invariants, are examples of mock modular forms. They have a quite complicated modular anomaly expressed as a sum over three different types of trees weighted by generalized error functions and their derivatives. We show that this anomaly can be significantly simplified, which in turn simplfies finding the corresponding mock modular generating functions.

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