2021/10/11 by Aradhita Chattopadhyaya, Jan Manschot, Swapnamay Mondal · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Black brane #Compactification (mathematics) #Cosmology and Gravitation Theories #Dilaton #Entropy (arrow of time) #Extremal black hole #Fibration #Geometry #Holomorphic function #Mathematical physics #Mathematics #Modular design #Modular form #Modular invariance #Particle physics theoretical and experimental studies #Partition function (quantum field theory) #Physics #Pure mathematics #Quantum mechanics #Scaling #String theory #Theoretical physics #hep-th #math.NT
paper · pdf · open access · doi:10.1007/jhep03(2022)001
published in Journal of High Energy Physics 2022(3) (Springer Nature) · 52 pages
arxiv created 2021/10/11 · openalex publication_date 2022/03/01 · arxiv updated 2022/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Scaling black holes are solutions of supergravity with multiple black hole singularities, which can be adiabatically connected to a single center black hole solution. We develop techniques to determine partition functions for such scaling black holes, if each constituent carries a non-vanishing magnetic charge corresponding to a D4-brane in string theory, or equivalently M5-brane in M-theory. For three constituents, we demonstrate that the partition function is a mock modular form of depth two, and we determine the appropriate non-holomorphic completion using generalized error functions. From the four-dimensional perspective, the modular parameter is the axion-dilaton, and our results show that S-duality leaves this subset of the spectrum invariant. From the five-dimensional perspective, the modular parameter is the complex structure of a torus T2, and the scaling black holes are dual to states in the dimensional reduction of the M5-brane worldvolume theory to T2. As a case study, we specialize the compactification manifold to a K3 fibration, and explicitly evaluate holomorphic parts of partition functions.