Cutting corners: exciting and magical bounds from the cusp bootstrap
Abstract
An illuminating probe of the dynamics of a line defect is the global geometry of its worldline. For a conformal line defect in a conformal field theory, sharp corners in the worldline, i.e. cusps, host dynamical degrees of freedom characterized in part by a spectrum of scaling dimensions, called cusp anomalous dimensions. We present various general bounds on cusp anomalous dimensions following from unitarity and cutting-and-gluing consistency of different defect geometries. We first establish, for cusps involving conjugate defects, that level crossings upon varying the cusp angle are forbidden between the lightest singlet cusp and any non-singlet cusp, proving that singlet cusps are the lightest. Then, we study line defects arranged in a rectangular geometry, which are subject to bootstrap constraints reminiscent of the spinless modular bootstrap. We find an analytic ``magic" functional that produces an optimal and universal lower bound on the dimension of a right angle bare cusp in terms of the universal defect Casimir energy between the corresponding defect and its conjugate in flat space.
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BibTeX
@misc{lanzetta2026cutting,
title = {{Cutting corners: exciting and magical bounds from the cusp bootstrap}},
author = {Ryan A. Lanzetta and Ian Moult and Yifan Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04041},
eprint = {2609.04041},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04041},
}
RIS
TY - UNPB
TI - Cutting corners: exciting and magical bounds from the cusp bootstrap
AU - Ryan A. Lanzetta
AU - Ian Moult
AU - Yifan Wang
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.04041
UR - https://arxiv.org/abs/2609.04041
AB - An illuminating probe of the dynamics of a line defect is the global geometry of its worldline. For a conformal line defect in a conformal field theory, sharp corners in the worldline, i.e. cusps, host dynamical degrees of freedom characterized in part by a spectrum of scaling dimensions, called cusp anomalous dimensions. We present various general bounds on cusp anomalous dimensions following from unitarity and cutting-and-gluing consistency of different defect geometries. We first establish, for cusps involving conjugate defects, that level crossings upon varying the cusp angle are forbidden between the lightest singlet cusp and any non-singlet cusp, proving that singlet cusps are the lightest. Then, we study line defects arranged in a rectangular geometry, which are subject to bootstrap constraints reminiscent of the spinless modular bootstrap. We find an analytic ``magic" functional that produces an optimal and universal lower bound on the dimension of a right angle bare cusp in terms of the universal defect Casimir energy between the corresponding defect and its conjugate in flat space.
ER -