We review recent developments in Jackiw–Teitelboim gravity. This is a simple solvable model of quantum gravity in two dimensions (that arises e.g. from the swave sector of higher dimensional gravity systems with spherical symmetry). Due to its solvability, it has proven to be a fruitful toy model to analyze important questions such as the relation between black holes and chaos, the role of wormholes in black hole physics and holography, and the way in which information that falls into a black hole can be recovered.
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Abstract 
A bstract We develop the gauge theory formulation of $$ \mathcal{N} $$ N = 1 JackiwTeitelboim supergravity in terms of the underlying OSp(12 , ℝ) supergroup, focusing on boundary dynamics and the exact structure of gravitational amplitudes. We prove that the BF description reduces to a superSchwarzian quantum mechanics on the holographic boundary, where boundaryanchored Wilson lines map to bilocal operators in the superSchwarzian theory. A classification of defects in terms of monodromies of OSp(12 , ℝ) is carried out and interpreted in terms of character insertions in the bulk. From a mathematical perspective, we construct the principal series representations of OSp(12 , ℝ) and show that whereas the corresponding Plancherel measure does not match the density of states of $$ \mathcal{N} $$ N = 1 JT supergravity, a restriction to the positive subsemigroup OSp + (12 , ℝ) yields the correct density of states, mirroring the analogous results for bosonic JT gravity. We illustrate these results with several gravitational applications, in particular computing the latetime complexity growth in JT supergravity.more » « less

A bstract We investigate the underlying quantum group symmetry of 2d Liouville and dilaton gravity models, both consolidating known results and extending them to the cases with $$ \mathcal{N} $$ N = 1 supersymmetry. We first calculate the mixed parabolic representation matrix element (or Whittaker function) of U q ( $$ \mathfrak{sl} $$ sl (2 , ℝ)) and review its applications to Liouville gravity. We then derive the corresponding matrix element for U q ( $$ \mathfrak{osp} $$ osp (1  2 , ℝ)) and apply it to explain structural features of $$ \mathcal{N} $$ N = 1 Liouville supergravity. We show that this matrix element has the following properties: (1) its q → 1 limit is the classical OSp + (1  2 , ℝ) Whittaker function, (2) it yields the Plancherel measure as the density of black hole states in $$ \mathcal{N} $$ N = 1 Liouville supergravity, and (3) it leads to 3 j symbols that match with the coupling of boundary vertex operators to the gravitational states as appropriate for $$ \mathcal{N} $$ N = 1 Liouville supergravity. This object should likewise be of interest in the context of integrability of supersymmetric relativistic Toda chains. We furthermore relate Liouville (super)gravity to dilaton (super)gravity with a hyperbolic sine (pre)potential. We do so by showing that the quantization of the target space Poisson structure in the (graded) Poisson sigma model description leads directly to the quantum group U q ( $$ \mathfrak{sl} $$ sl (2 , ℝ)) or the quantum supergroup U q ( $$ \mathfrak{osp} $$ osp (1  2 , ℝ)).more » « less