Equivalences between 2D dilaton gravities, their asymptotic symmetries, and their holographic duals

Abstract

Dilaton gravities in two dimensions can be formulated as particular Poisson sigma models. Target space diffeomorphisms map different models to each other and establish a one-to-one correspondence between their classical solutions. We obtain a general form of such diffeomorphisms in Lorentzian and Euclidean signatures and use them to extend known holographic results, including the Schwarzian action on the asymptotic boundary, from JT to a large class of dilaton gravity models.

Finite charges from the bulk action

“…We apply this prescription to two dimensional dilaton gravity theories and three dimensional Einstein gravity (with or without a cosmological constant) with leaky boundary conditions. These lower dimensional theories are widely used as toy models of quantum gravity, tractable examples of black hole evaporation, and concrete examples of holographic dualities [32,[38][39][40][41][42][43][44][45][46][47][48][49]. The resulting charges (1.1) are not only finite, but also symplectic in the sense that the codimension-2 form is independent of the coordinate r used to define the limiting procedure (consistent with previous results obtained in various gauges [36,37,[50][51][52][53]).…”