Electric/Magnetic Newton-Hooke and Carroll Jackiw-Teitelboim Gravity

Non-relativistic and Carrollian limits of Jackiw-Teitelboim gravity

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 …

Newton-Hooke/Carrollian expansions of (A)dS and Chern-Simons gravity

We construct finite- and infinite-dimensional non-relativistic extensions of the Newton-Hooke and Carroll (A)dS algebras using the algebra expansion method, starting from the (anti-)de Sitter relativistic algebra in D dimensions. These algebras are also shown to be embedded in different affine Kac-Moody algebras. In the three-dimensional case, we construct Chern-Simons actions invariant under these symmetries. This leads to a sequence of non-relativistic gravity theories, where the simplest examples correspond to extended Newton-Hooke and extended (post-)Newtonian gravity together with their C…

Carrollian and Non-relativistic Jackiw-Teitelboim Supergravity

We present non- and ultra-relativistic Jackiw-Teitelboim (JT) supergravity as metric BF theories based on the extended Newton-Hooke and extended AdS Carroll superalgebras in two spacetime dimensions, respectively. The extended Newton-Hooke structure, and, in particular, the invariant metric necessary for the BF construction of non-relativistic JT supergravity, is obtained by performing an expansion of the $\mathcal{N}=2$ AdS$_2$ superalgebra. Subsequently, we introduce the extended AdS$_2$ Carroll superalgebra, and the associated invariant metric, as a suitable redefinition of the extended New…

二维Carroll膨胀子超引力

Carroll dilaton supergravity in two dimensions

本文构造并讨论了二维N=1和N=2 Carroll膨胀子超引力，将其应用于超对称Carroll-Jackiw-Teitelboim模型并探讨边界条件，发现N=2版本存在“民主”与“专制”两种形式。

Asymptotic symmetries in Carrollian theories of gravity

Asymptotic symmetries in Carrollian gravitational theories in 3+1 space and time dimensions obtained from "magnetic" and "electric" ultrarelativistic contractions of General Relativity are analyzed. In both cases, parity conditions are needed to guarantee a finite symplectic term, in analogy with Einstein gravity. For the magnetic contraction, when Regge-Teitelboim parity conditions are imposed, the asymptotic symmetries are described by the Carroll group. With Henneaux-Troessaert parity conditions, the asymptotic symmetry algebra corresponds to a BMS-like extension of the Carroll algebra. For…

Carroll 膨胀引力离散 BF 形式中的和乐与边界对称性

Holonomies and Boundary Symmetries in the Discrete BF Formulation of Carroll Dilaton Gravity

基于 BF 型规范结构，利用格点上的和乐变量构建二维 Carroll 膨胀引力的离散实现，通过边界条件导出渐近对称性，得到仿射 Carroll 代数及其共形约化，为离散 Jackiw-Teitelboim 引力的超相对论对应。