Timelike entanglement entropy with gravitational anomaly from complexified geometry
Abstract
We investigate the timelike entanglement entropy (TEE) in a two-dimensional conformal field theory with a gravitational anomaly, cL≠ cR, dual to topologically massive gravity in AdS3. Holographically, the TEE is determined by the on-shell action of a massive spinning particle on a single complex geodesic anchored at the endpoints of the timelike interval. This action consists of the complex geodesic length and the twist of a parallel-transported normal frame. We carry out the computation in Poincaré AdS3, non-extremal and extremal rotating BTZ backgrounds, and provide an equivalent Chern-Simons derivation in which the bulk connection stays real while only the saddle of the Wilson-line probe becomes complex. In each case, the holographic result matches the corresponding TEE in dual field theory. The real part of the TEE is fixed unambiguously whereas its imaginary part depends on the boundary iε prescription and the orientation of the interval. In the bulk, the dependence on orientation reflects an ambiguity in the choice of framing. Along the complex geodesic, the residual frame group becomes SO(2,ℂ)≃ℂ*, so the endpoint conditions determine the frame twist only up to integer multiples of 2πi. The difference between the two orientations, (cL−cR)/6 iπ, is fixed entirely by the gravitational anomaly and persists for the Rényi pseudo-entropies.
Related
- Modular Flow and Holographic Timelike Entanglement Entropy in AdS and Flat Holography
- Aspects of holographic timelike entanglement entropy in black hole backgrounds
- Covariant Holographic Entanglement Entropy Inversion to Reconstruct Bulk Geometry
- Cohomological Aspects of Entanglement Entropy: From Information Theory to Noncommutative Geometry
- Timelike Entanglement from Spacetime Density Matrices: A Lattice Realization
BibTeX
@misc{lim2026timelike,
title = {{Timelike entanglement entropy with gravitational anomaly from complexified geometry}},
author = {Minwoo Lim and Himanshu Parihar and Junggi Yoon},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.23514},
eprint = {2610.23514},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.23514},
}
RIS
TY - UNPB
TI - Timelike entanglement entropy with gravitational anomaly from complexified geometry
AU - Minwoo Lim
AU - Himanshu Parihar
AU - Junggi Yoon
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.23514
UR - https://arxiv.org/abs/2610.23514
AB - We investigate the timelike entanglement entropy (TEE) in a two-dimensional conformal field theory with a gravitational anomaly, c_L≠ c_R, dual to topologically massive gravity in AdS_3. Holographically, the TEE is determined by the on-shell action of a massive spinning particle on a single complex geodesic anchored at the endpoints of the timelike interval. This action consists of the complex geodesic length and the twist of a parallel-transported normal frame. We carry out the computation in Poincaré AdS_3, non-extremal and extremal rotating BTZ backgrounds, and provide an equivalent Chern-Simons derivation in which the bulk connection stays real while only the saddle of the Wilson-line probe becomes complex. In each case, the holographic result matches the corresponding TEE in dual field theory. The real part of the TEE is fixed unambiguously whereas its imaginary part depends on the boundary iε prescription and the orientation of the interval. In the bulk, the dependence on orientation reflects an ambiguity in the choice of framing. Along the complex geodesic, the residual frame group becomes SO(2,ℂ)≃ℂ^*, so the endpoint conditions determine the frame twist only up to integer multiples of 2πi. The difference between the two orientations, (c_L−c_R)/6 iπ, is fixed entirely by the gravitational anomaly and persists for the Rényi pseudo-entropies.
ER -