PreprintarXiv licencearXiv
Covering Surfaces, Conical-Defect Continuation, and Multi-Entropy at Arbitrary Genus
Abstract
We derive normalized geometric factors for permutation-twist correlators at arbitrary genus. For three uniformly ramified branch values, hypergeometric uniformization shows that the real part of the continued conical-defect exponent equals the covering-space anomaly factor. Its imaginary part is an Euler-characteristic Weyl phase. We extend the normalization to additional branch values, derive higher replica-index corrections to the geometric multi-entropy, and state the extra condition required for a holographic limit. A reducible conformal/topological example demonstrates why large central charge alone does not fix the complete entanglement result.
Related
- Rényi Phase Transitions and Analytic Continuation to the von Neumann Entropy
- Thermodynamics of arbitrary spherical surfaces in FLRW spacetimes
- Explicit Boundary-Entropy Deficits in the XX Spin Chain with arbitrary boundary fields
- Obstruction to local entropy laws on arbitrary black-hole cuts in five-dimensional Einstein--Gauss--Bonnet gravity
- Haar-Bayesian Pure-State Prediction under Relative-Entropy Loss: Arbitrary-Effect Reduction and Global Optimality
BibTeX
@misc{ma2026covering,
title = {{Covering Surfaces, Conical-Defect Continuation, and Multi-Entropy at Arbitrary Genus}},
author = {Chen-Te Ma},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38208},
eprint = {2610.38208},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38208},
}
RIS
TY - UNPB
TI - Covering Surfaces, Conical-Defect Continuation, and Multi-Entropy at Arbitrary Genus
AU - Chen-Te Ma
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38208
UR - https://arxiv.org/abs/2610.38208
AB - We derive normalized geometric factors for permutation-twist correlators at arbitrary genus. For three uniformly ramified branch values, hypergeometric uniformization shows that the real part of the continued conical-defect exponent equals the covering-space anomaly factor. Its imaginary part is an Euler-characteristic Weyl phase. We extend the normalization to additional branch values, derive higher replica-index corrections to the geometric multi-entropy, and state the extra condition required for a holographic limit. A reducible conformal/topological example demonstrates why large central charge alone does not fix the complete entanglement result.
ER -