Holonomy Separation and Anyonic Hair in AdS3
Abstract
Three-dimensional Einstein gravity and Chern-Simons-Higgs matter both admit Chern-Simons descriptions, but their holonomies encode different physics. We prove that charge conjugation reverses the vortex winding n→−n while leaving the metric and the gravitational connections pointwise unchanged, so every closed gravitational holonomy character, the BTZ charges, the Bañados data and the leading geometric mixed-state hierarchy are exactly even in n. On a fixed marked Euclidean replica filling the same change of variables gives Zq[n;𝒥+]=Zq[−n;𝒥+], so the uncharged Rényi hierarchy, the Faulkner-Lewkowycz-Maldacena one-loop correction, the renormalized generalized entropy and the quantum extremal surfaces coincide for the two orientations. The complementary sector is fixed exactly: with an Aharonov-Bohm angle μ conjugate to the entangling-region charge, Zq[n;μ]=Zq[−n;−μ], so the symmetry-resolved spectrum obeys 𝒵q(𝒬;n)=𝒵q(−𝒬;−n) and every odd charged cumulant reverses with the winding. The orientation is therefore stored entirely in the charge asymmetry of the entanglement spectrum, and is read at topological order by a linked charged matter line. The pair is a bulk logical qubit on which the neutral gravitational-replica algebra acts as a multiple of the identity. Exact BTZ cross sections show that the purification plateau and the entanglement wedge disconnection transition are orientation blind, the latter closing with the cutoff-independent jump (c/3)log(1+√2). Numerical Bogomolny solutions verify odd flux and even energy and spin; used as linearized charge-matching data they give the even asymptotic shifts δM̂=16πGv2|n| and |δĵ|=16πGv2n2/(mL) and, conditionally, a finite continuous winding envelope.
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BibTeX
@misc{ghosh2026holonomy,
title = {{Holonomy Separation and Anyonic Hair in AdS$_3$}},
author = {Kumar Ghosh},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29562},
eprint = {2609.29562},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29562},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Holonomy Separation and Anyonic Hair in AdS_3
AU - Kumar Ghosh
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.29562
UR - https://arxiv.org/abs/2609.29562
AB - Three-dimensional Einstein gravity and Chern-Simons-Higgs matter both admit Chern-Simons descriptions, but their holonomies encode different physics. We prove that charge conjugation reverses the vortex winding n→−n while leaving the metric and the gravitational connections pointwise unchanged, so every closed gravitational holonomy character, the BTZ charges, the Bañados data and the leading geometric mixed-state hierarchy are exactly even in n. On a fixed marked Euclidean replica filling the same change of variables gives Z_q[n;𝒥_+]=Z_q[−n;𝒥_+], so the uncharged Rényi hierarchy, the Faulkner-Lewkowycz-Maldacena one-loop correction, the renormalized generalized entropy and the quantum extremal surfaces coincide for the two orientations. The complementary sector is fixed exactly: with an Aharonov-Bohm angle μ conjugate to the entangling-region charge, Z_q[n;μ]=Z_q[−n;−μ], so the symmetry-resolved spectrum obeys 𝒵_q(𝒬;n)=𝒵_q(−𝒬;−n) and every odd charged cumulant reverses with the winding. The orientation is therefore stored entirely in the charge asymmetry of the entanglement spectrum, and is read at topological order by a linked charged matter line. The pair is a bulk logical qubit on which the neutral gravitational-replica algebra acts as a multiple of the identity. Exact BTZ cross sections show that the purification plateau and the entanglement wedge disconnection transition are orientation blind, the latter closing with the cutoff-independent jump (c/3)log(1+√2). Numerical Bogomolny solutions verify odd flux and even energy and spin; used as linearized charge-matching data they give the even asymptotic shifts δM̂=16πGv^2|n| and |δĵ|=16πGv^2n^2/(mL) and, conditionally, a finite continuous winding envelope.
ER -