Non-relativistic and Carrollian limits of Jackiw-Teitelboim gravity

TL;DR

This paper develops non-relativistic and Carrollian limits of Jackiw-Teitelboim gravity, analyzing their boundary duals, symmetries, and geometric structures, and resolving divergences through BF theory formulations.

Contribution

It introduces a consistent method to obtain non-relativistic and Carrollian JT gravity from BF theory, including boundary actions and symmetry analysis.

Findings

Constructed non-relativistic and Carrollian JT gravity models.

Derived boundary dual actions, including the non-relativistic Schwarzian.

Analyzed asymptotic symmetries and conserved charges.

Abstract

We construct the non-relativistic and Carrollian versions of Jackiw-Teitelboim gravity. In the second order formulation, there are no divergences in the non-relativistic and Carrollian limits. Instead, in the first order formalism there are divergences that can be avoided by starting from a relativistic BF theory with (A)dS2$\times\mathbb{R}$ gauge algebra. We show how to define the boundary duals of the gravity actions using the method of non-linear realisations and suitable Inverse Higgs constraints. In particular, the non-relativistic version of the Schwarzian action is constructed in this way. We derive the asymptotic symmetries of the theory, as well as the corresponding conserved charges and Newton-Cartan geometric structure. Finally, we show how the same construction applies to the Carrollian case.