Holonomies and boundary symmetries in discrete Jackiw–Teitelboim gravity
- 1Istanbul Technical University
Abstract
We develop a fully discrete and non-perturbative realization of two-dimensional Jackiw–Teitelboim (JT) gravity as an sl(2,ℝ) BF theory. Using group-valued holonomies and Lie-algebra-valued dilatons, the bulk theory is shown to be purely topological, with all physical information encoded at the boundary. We analyze admissible discrete boundary conditions and derive the corresponding asymptotic symmetry algebras directly at the lattice level, including an affine Kac–Moody symmetry and its Brown–Henneaux reduction to a Virasoro algebra, together with the associated Virasoro–dilaton structure. A precise operator product expansion (OPE) dictionary is established by taking the controlled continuum limit of the discrete Poisson brackets. Beyond asymptotic symmetries, we provide an effective boundary description and a representation-theoretic quantization organized by monodromy sectors. Within this discrete framework, black hole entropy follows from gauge-invariant holonomy data and is expressed in terms of the dilaton Casimir, reproducing the Bekenstein–Hawking result within a framework that does not require an explicit Schwarzian action.
Related
- Holonomies and Boundary Symmetries in the Discrete BF Formulation of Carroll Dilaton Gravity
- Confining Random Potential Quantum Mechanics for Jackiw-Teitelboim Gravity
- Logarithmic supertranslations as asymptotic symmetries of gravity at null infinity
- Discrete symmetries of modified Teukolsky equations
- Higher-form Symmetries of Linearized Gravity in Maximally Symmetric Spaces
BibTeX
@article{ozer2026holonomies,
title = {{Holonomies and boundary symmetries in discrete Jackiw–Teitelboim gravity}},
author = {H. T. Özer and Aytül Filiz},
journal = {The European Physical Journal C},
year = {2026},
month = nov,
doi = {10.1140/epjc/s10052-026-16522-1},
url = {https://link.springer.com/article/10.1140/epjc/s10052-026-16522-1},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Holonomies and boundary symmetries in discrete Jackiw–Teitelboim gravity
AU - H. T. Özer
AU - Aytül Filiz
PY - 2026
DA - 2026/11/06
JO - The European Physical Journal C
DO - 10.1140/epjc/s10052-026-16522-1
UR - https://link.springer.com/article/10.1140/epjc/s10052-026-16522-1
AB - We develop a fully discrete and non-perturbative realization of two-dimensional Jackiw–Teitelboim (JT) gravity as an sl(2,ℝ) BF theory. Using group-valued holonomies and Lie-algebra-valued dilatons, the bulk theory is shown to be purely topological, with all physical information encoded at the boundary. We analyze admissible discrete boundary conditions and derive the corresponding asymptotic symmetry algebras directly at the lattice level, including an affine Kac–Moody symmetry and its Brown–Henneaux reduction to a Virasoro algebra, together with the associated Virasoro–dilaton structure. A precise operator product expansion (OPE) dictionary is established by taking the controlled continuum limit of the discrete Poisson brackets. Beyond asymptotic symmetries, we provide an effective boundary description and a representation-theoretic quantization organized by monodromy sectors. Within this discrete framework, black hole entropy follows from gauge-invariant holonomy data and is expressed in terms of the dilaton Casimir, reproducing the Bekenstein–Hawking result within a framework that does not require an explicit Schwarzian action.
SN - 1434-6052
ER -