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.
Highlights
Jackiw-Teitelboim (JT) gravity [1,2,3,4] features prominently in classical and quantum gravity as a convenient toy model to elucidate conceptual problems while keeping the technical ones at a bare minimum
We provide an overview of all Lie algebras of low dimension that admit an invariant metric in appendix A
In addition to the well-known homogeneous spaces and their BF theories mentioned in the previous subsection there exists another homogeneous space based on the symmetry algebra sl(2, R) which is the light cone of three dimensional Minkowski space seen as 2d manifold
Summary
Jackiw-Teitelboim (JT) gravity [1,2,3,4] features prominently in classical and quantum gravity as a convenient toy model to elucidate conceptual problems while keeping the technical ones at a bare minimum. See [30] for a review on further aspects of two-dimensional (2d) dilaton gravity, including numerous generalizations of JT gravity, like the Callan-Giddings-Harvey-Strominger (CGHS) model [31]. None of these generalizations so far gave up the assumption of (pseudo-)Riemannian metrics (or a corresponding Cartan formulation). For applications or toy models of non-relativistic holography it is of interest to consider singular limits of JT gravity to, say, Carrollian or Galilean spacetimes. Some of its limits may lead to Lie algebras without metric Since these subtleties will be relevant for the remaining work, we set the stage by providing a rather detailed reminder of BF theories. We follow [44] where further details are provided (see the review [45]; especially relevant is section 6 on Schwarz type topological gauge theories)
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