Non-relativistic and Carrollian limits of Jackiw-Teitelboim gravity

TL;DR

The paper develops non-relativistic and Carrollian limits of Jackiw-Teitelboim gravity using BF formulations with (A)dS2×R gauge algebras, constructing finite bulk actions and well-defined boundary duals through non-linear realisations and inverse Higgs constraints. It derives NR and Carrollian bulk dynamics, identifies corresponding Newton-Cartan and Carrollian geometries, and shows that NR/Carrollian Schwarzian actions arise as boundary theories. The authors compute asymptotic symmetries and conserved charges, revealing extended algebras such as warped Virasoro and their complexifications, and demonstrate how Drinfeld-Sokolov reduction underpins the Schwarzian boundary dynamics. The work provides a unified framework linking NR/Carrollian gravity, boundary actions, and symmetry structures, with potential implications for SYK-related holography and NR/Carrollian gravitational holography.

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.