Cusp regularization with spin structures and gravitational anomalies
Abstract
The family of SL(2,ℤ) black holes has an accumulation point corresponding to a cusped geometry, which causes the sum over black holes to diverge. We extend cusp regularization to the sum over geometries compatible with a fixed boundary spin structure. For cL=cR, including the cusp as a counterterm cancels the leading divergence for each of the three even boundary spin structures. The required subtraction is the same in all three sectors and is two thirds of the bosonic one. We further show that gravitational anomalies cause cancellations between black hole contributions, removing the leading cusp divergence except at cL−cR=0,±24 in pure gravity and cL−cR=0,±12 in 𝒩=(1,1) supergravity. We also derive the spin structure dependent anomaly phases responsible for these cancellations.
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BibTeX
@misc{tabor2026cusp,
title = {{Cusp regularization with spin structures and gravitational anomalies}},
author = {Elisa Tabor and Cynthia Yan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36028},
eprint = {2610.36028},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36028},
}
RIS
TY - UNPB
TI - Cusp regularization with spin structures and gravitational anomalies
AU - Elisa Tabor
AU - Cynthia Yan
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.36028
UR - https://arxiv.org/abs/2610.36028
AB - The family of SL(2,ℤ) black holes has an accumulation point corresponding to a cusped geometry, which causes the sum over black holes to diverge. We extend cusp regularization to the sum over geometries compatible with a fixed boundary spin structure. For c_L=c_R, including the cusp as a counterterm cancels the leading divergence for each of the three even boundary spin structures. The required subtraction is the same in all three sectors and is two thirds of the bosonic one. We further show that gravitational anomalies cause cancellations between black hole contributions, removing the leading cusp divergence except at c_L−c_R=0,±24 in pure gravity and c_L−c_R=0,±12 in 𝒩=(1,1) supergravity. We also derive the spin structure dependent anomaly phases responsible for these cancellations.
ER -