T(T)over-bar-deformation and Liouville gravity

We consider a gravitational perturbation of the Jackiw-Teitelboim (JT) gravity with an arbitrary dilaton potential and study the condition under which the quadratic action can be seen as a T (T) over bar -deformation of the matter action. As a special case, the flat-space JT gravity discussed by Dubovsky et al.[arXiv:1706.06604] is included. Another interesting example is a hyperbolic dilaton potential. This case is equivalent to a classical Liouville gravity with a negative cosmological constant and then a T (T) over bar -deformation of the matter action with a finite coupling is realized as a gravitational perturbation on AdS(2). (C) 2020 The Authors. Published by Elsevier B.V.