Virasoro Zero-Mode Flow in Critical Topologically Massive Gravity: Logarithmic Correlators and Partition Function Grading
Abstract
We study the rank-two logarithmic sector of critical Topologically Massive Gravity through the Virasoro zero-mode action U(s,s̅)=e−sL0−s̅L̅0. Writing L0=h1+1/2N and L̅0=h̅1+1/2N, with N2=0, separates the semisimple conformal grading from the nilpotent mixing of the logarithmic pair. We apply the Virasoro zero-mode action to logarithmic two-point functions and to the conformal grading of the logarithmic contribution to the one-loop partition function. For the correlators, the semisimple part generates the ordinary conformal power law, while the nilpotent mixing governed by the combination s+s̅ produces the characteristic logarithmic dependence. For the critical-TMG weights (h,h̅)=(2,0), this gives a holomorphic power law together with logarithmic dependence on the full Euclidean separation. For the partition function, the relations q=e−s and q̅=e−s̅ express its conventional multiplicative grading in terms of the additive parameters of the same Virasoro zero-mode action, providing an exact reparameterization of the established one-loop result. The two applications capture complementary information: logarithmic correlators resolve the off-diagonal Jordan mixing, whereas the ordinary graded trace organizes conformal weights, multiplicities, and descendant content without separately resolving the nilpotent matrix element. The Virasoro zero-mode action therefore provides a unified representation-theoretic description of these boundary structures in critical TMG.
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BibTeX
@misc{mvondoshe2026virasoro,
title = {{Virasoro Zero-Mode Flow in Critical Topologically Massive Gravity: Logarithmic Correlators and Partition Function Grading}},
author = {Yannick Mvondo-She},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.03649},
eprint = {2605.03649},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.03649},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Virasoro Zero-Mode Flow in Critical Topologically Massive Gravity: Logarithmic Correlators and Partition Function Grading
AU - Yannick Mvondo-She
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2605.03649
UR - https://arxiv.org/abs/2605.03649
AB - We study the rank-two logarithmic sector of critical Topologically Massive Gravity through the Virasoro zero-mode action U(s,s̅)=e^−sL_0−s̅L̅_0. Writing L_0=h1+1/2N and L̅_0=h̅1+1/2N, with N^2=0, separates the semisimple conformal grading from the nilpotent mixing of the logarithmic pair. We apply the Virasoro zero-mode action to logarithmic two-point functions and to the conformal grading of the logarithmic contribution to the one-loop partition function. For the correlators, the semisimple part generates the ordinary conformal power law, while the nilpotent mixing governed by the combination s+s̅ produces the characteristic logarithmic dependence. For the critical-TMG weights (h,h̅)=(2,0), this gives a holomorphic power law together with logarithmic dependence on the full Euclidean separation. For the partition function, the relations q=e^−s and q̅=e^−s̅ express its conventional multiplicative grading in terms of the additive parameters of the same Virasoro zero-mode action, providing an exact reparameterization of the established one-loop result. The two applications capture complementary information: logarithmic correlators resolve the off-diagonal Jordan mixing, whereas the ordinary graded trace organizes conformal weights, multiplicities, and descendant content without separately resolving the nilpotent matrix element. The Virasoro zero-mode action therefore provides a unified representation-theoretic description of these boundary structures in critical TMG.
ER -