2025/10/22 by Douglas Stanford, Stanford, Douglas, Cynthia Yan +1
Physics and Astronomy · #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #Quantum Electrodynamics and Casimir Effect
paper · pdf · doi:10.48550/arxiv.2510.19920
Three dimensional hyperbolic manifolds have accumulation points in the spectrum of their volumes, leading to a divergence in the sum over topologies. The limit points are cusped hyperbolic manifolds, and we propose to renormalize the sum by including the cusped manifold as a counterterm. This gives a reinterpretation of the zeta-function regularization procedure used by Maloney and Witten in the sum over SL(2,Z) black holes. For pure N = 1 supergravity, cusps with even spin structure can be used in a similar way. Cusps with odd spin structure are not needed to cancel any divergence, but they find an application by making the index nonzero.