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arXiv · 2510.19920

Cusps in 3d gravity

Douglas Stanford·Cynthia Yan
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Abstract

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.

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Douglas Stanford, Cynthia Yan. 2025-10-22. Cusps in 3d gravity. https://arxiv.org/abs/2510.19920

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