Gravitational perturbations as $T\bar{T}$-deformations in 2D dilaton gravity systems

TL;DR

This work demonstrates that gravitational perturbations in 2D dilaton gravity with matter can, under specific conditions, be recast as $T\bar{T}$-deformations of the matter action, thereby dressing the matter sector nonperturbatively. The authors derive the quadratic action for metric and dilaton fluctuations around a vacuum, connect the resulting dynamics to a $T\bar{T}$-type term, and illustrate the mechanism in both the flat-space JT case and a broader class with $U'(\phi)\neq 0$, including the Almheiri–Polchinski model. The key contribution is showing that gravitational perturbations provide a nontrivial, nonlocal deformation of the matter sector that preserves integrability structures in 2D, with potential implications for AdS$_2$/CFT$_1$ holography and curved-space $T\bar{T}$-duality. The work also lays out future directions, such as boundary terms, finite-volume spectra, and extensions to non-conformal matter and Yang–Baxter deformations, which could deepen the connection between gravity in two dimensions and solvable quantum field theories.

Abstract

We consider gravitational perturbations of 2D dilaton gravity systems and show that these can be recast into $T\bar{T}$-deformations (at least) under certain conditions, where $T$ means the energy-momentum tensor of the matter field coupled to a dilaton gravity. In particular, the class of theories under this condition includes a Jackiw-Teitelboim (JT) theory with a negative cosmological constant including conformal matter fields. This is a generalization of the preceding work on the flat-space JT gravity by S. Dubovsky, V. Gorbenko and M. Mirbabayi [arXiv:1706.06604].