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Limits of JT gravity

Daniel Grumiller, Jelle Hartong, Stefan Prohazka, Jakob Salzer

TL;DR

This work develops a cohesive BF-theory framework to derive and relate multiple JT gravity limits, including Newton–Cartan and Carrollian dilaton gravities in two dimensions and a light-cone theory in 3D. By imposing boundary conditions that bind boundary connections to boundary scalars, it recasts boundary dynamics as a particle on a group manifold and, through Hamiltonian reduction, as Schwarzian- or warped-Schwarzian-type actions; notably, AdS–Carroll gravity yields a twisted warped boundary action. Across AdS/dS, light-cone, Galilean, Carrollian, and other kinematical limits, the authors map out the algebraic structure, invariant metrics, and resulting boundary theories, highlighting how central extensions restore metric BF formulations in contractions. The paper also outlines concrete applications and generalizations, including potential JT/SYK-type dualities, holographic connections to higher dimensions, and the Poisson–Sigma-model perspective for nonlinear deformations. Overall, it provides a unifying route to non-Riemannian dilaton gravities and their Schwarzian-like boundary dynamics within a 2D BF setup, with broad consequences for holography, boundary dynamics, and nonrelativistic gravity.

Abstract

We construct various limits of JT gravity, including Newton-Cartan and Carrollian versions of dilaton gravity in two dimensions as well as a theory on the three-dimensional light cone. In the BF formulation our boundary conditions relate boundary connection with boundary scalar, yielding as boundary action the particle action on a group manifold or some Hamiltonian reduction thereof. After recovering in our formulation the Schwarzian for JT, we show that AdS-Carroll gravity yields a twisted warped boundary action. We comment on numerous applications and generalizations.

Limits of JT gravity

TL;DR

This work develops a cohesive BF-theory framework to derive and relate multiple JT gravity limits, including Newton–Cartan and Carrollian dilaton gravities in two dimensions and a light-cone theory in 3D. By imposing boundary conditions that bind boundary connections to boundary scalars, it recasts boundary dynamics as a particle on a group manifold and, through Hamiltonian reduction, as Schwarzian- or warped-Schwarzian-type actions; notably, AdS–Carroll gravity yields a twisted warped boundary action. Across AdS/dS, light-cone, Galilean, Carrollian, and other kinematical limits, the authors map out the algebraic structure, invariant metrics, and resulting boundary theories, highlighting how central extensions restore metric BF formulations in contractions. The paper also outlines concrete applications and generalizations, including potential JT/SYK-type dualities, holographic connections to higher dimensions, and the Poisson–Sigma-model perspective for nonlinear deformations. Overall, it provides a unifying route to non-Riemannian dilaton gravities and their Schwarzian-like boundary dynamics within a 2D BF setup, with broad consequences for holography, boundary dynamics, and nonrelativistic gravity.

Abstract

We construct various limits of JT gravity, including Newton-Cartan and Carrollian versions of dilaton gravity in two dimensions as well as a theory on the three-dimensional light cone. In the BF formulation our boundary conditions relate boundary connection with boundary scalar, yielding as boundary action the particle action on a group manifold or some Hamiltonian reduction thereof. After recovering in our formulation the Schwarzian for JT, we show that AdS-Carroll gravity yields a twisted warped boundary action. We comment on numerous applications and generalizations.

Paper Structure

This paper contains 27 sections, 108 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. 2d gauge theories of gravity
  3. BF theories
  4. Geometric interpretation
  5. Limits of JT gravity
  6. AdS and dS BF theory
  7. BF on the light cone
  8. Kinematical limits of BF theories
  9. Newton--Cartan dilaton gravity and Carroll dilaton gravity
  10. Metric BF theories and their limits
  11. Metrics and limits
  12. Flat space dilaton gravity
  13. Summary
  14. Boundary actions of kinematical BF theories
  15. Particle on group manifold
  16. ...and 12 more sections

Figures (3)

  • Figure 1: Penrose diagrams for AdS$_2$ (left) and dS$_2$ (right).
  • Figure 2: Two-dimensional future light cone of three-dimensional Minkowski space with vertex removed. Topologically, this is a strip like (A)dS$_2$.
  • Figure 3: Kinematical limits of (anti-)de Sitter: non-relativistic/Galilean ($\hat{c}=\frac{1}{c} \to 0$); flat ($\hat{\Lambda} \to 0$); ultra-relativistic/Carrollian ($\hat{C} \to 0$). Arrows with two lines imply there are two different limits, depending on the sign of the cosmological constant.