Complexified Virasoro Zero-Mode Flow and the Logarithmic Graviton at the Chiral Point
Abstract
We investigate the relation between Virasoro zero-mode evolution and the bulk logarithmic graviton in topologically massive gravity at the chiral point. By introducing additive coordinates adapted to the global time and radial dependence of the logarithmic mode, we obtain the expression y(s,s̅) = −s+ln2 −ln (1+e−(s+s̅)), s=ρ+iτ, s̅=ρ−iτ. This relation provides a direct bulk realization of the additive coordinates previously associated with the joint Virasoro zero-mode evolution. Near the AdS3 boundary, the logarithmic coefficient becomes linear in s up to an additive constant and exponentially suppressed corrections, while its exact finite-radius dependence is governed by the diagonal combination s+s̅=2ρ. Upon complexification of the radial coordinate, this combination also organizes the periodic branch structure underlying the previously established bulk monodromy of the logarithmic graviton. The same diagonal coordinate controls the nilpotent part of the Virasoro zero-mode representation, providing a common additive-coordinate description of the representation-theoretic Jordan structure and the radial analytic structure of the bulk solution. The corresponding operations remain distinct: finite zero-mode evolution is algebraic, whereas bulk monodromy arises from analytic continuation and winding of the multivalued gravitational solution.
Related
- The classical two-loop amplitude at leading logarithmic accuracy for graviton emission in multi-Regge kinematics
- Bulk Monodromy of Logarithmic Graviton Descendants in Critical Topologically Massive Gravity
- Virasoro Zero-Mode Flow in Critical Topologically Massive Gravity: Logarithmic Correlators and Partition Function Grading
- Gravitational multipoles, antipodal matching relations, and the logarithmic soft graviton theorem
- Only the immortal can (almost) flock while turning: Two-dimensional chiral immortal flocks, time crystals and non-universal sub-logarithmic roughness
BibTeX
@misc{mvondoshe2026complexified,
title = {{Complexified Virasoro Zero-Mode Flow and the Logarithmic Graviton at the Chiral Point}},
author = {Yannick Mvondo-She},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.16444},
eprint = {2606.16444},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.16444},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Complexified Virasoro Zero-Mode Flow and the Logarithmic Graviton at the Chiral Point
AU - Yannick Mvondo-She
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2606.16444
UR - https://arxiv.org/abs/2606.16444
AB - We investigate the relation between Virasoro zero-mode evolution and the bulk logarithmic graviton in topologically massive gravity at the chiral point. By introducing additive coordinates adapted to the global time and radial dependence of the logarithmic mode, we obtain the expression y(s,s̅) = −s+ln2 −ln (1+e^−(s+s̅)), s=ρ+iτ, s̅=ρ−iτ. This relation provides a direct bulk realization of the additive coordinates previously associated with the joint Virasoro zero-mode evolution. Near the AdS_3 boundary, the logarithmic coefficient becomes linear in s up to an additive constant and exponentially suppressed corrections, while its exact finite-radius dependence is governed by the diagonal combination s+s̅=2ρ. Upon complexification of the radial coordinate, this combination also organizes the periodic branch structure underlying the previously established bulk monodromy of the logarithmic graviton. The same diagonal coordinate controls the nilpotent part of the Virasoro zero-mode representation, providing a common additive-coordinate description of the representation-theoretic Jordan structure and the radial analytic structure of the bulk solution. The corresponding operations remain distinct: finite zero-mode evolution is algebraic, whereas bulk monodromy arises from analytic continuation and winding of the multivalued gravitational solution.
ER -