Eye-opening bounds on cusps
Abstract
We derive new nonperturbative inequalities on the cusp anomalous dimensions of conformal line defects. We impose reflection positivity, locality, and conformal invariance on a pair of cusps forming an ``eye'' geometry, deriving a novel condition on the cusp anomalous dimension which we refer to as conformal concavity. The resulting constraint is much stronger than the known angular concavity, and our derivation applies also to cusps involving distinct line defects. Remarkably, it directly links the smooth and fusion limits, yielding bounds on defect-changing operator dimensions, Casimir energies, and subleading fusion data. We thus uncover a new quantitative bridge between aspects of the local operator data and the fusion rules of line operators in conformal field theories.
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BibTeX
@misc{lanzetta2026eyeopening,
title = {{Eye-opening bounds on cusps}},
author = {Ryan A. Lanzetta and Ian Moult and Yifan Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04302},
eprint = {2609.04302},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04302},
}
RIS
TY - UNPB
TI - Eye-opening bounds on cusps
AU - Ryan A. Lanzetta
AU - Ian Moult
AU - Yifan Wang
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.04302
UR - https://arxiv.org/abs/2609.04302
AB - We derive new nonperturbative inequalities on the cusp anomalous dimensions of conformal line defects. We impose reflection positivity, locality, and conformal invariance on a pair of cusps forming an ``eye'' geometry, deriving a novel condition on the cusp anomalous dimension which we refer to as conformal concavity. The resulting constraint is much stronger than the known angular concavity, and our derivation applies also to cusps involving distinct line defects. Remarkably, it directly links the smooth and fusion limits, yielding bounds on defect-changing operator dimensions, Casimir energies, and subleading fusion data. We thus uncover a new quantitative bridge between aspects of the local operator data and the fusion rules of line operators in conformal field theories.
ER -