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 $T\overline{T}$-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 $T\overline{T}$-deformation of the matter action with a finite coupling is realized as a gravitational perturbation on AdS₂.

中文翻译：

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$Ť\overline{Ť}$变形和利维尔重力

我们考虑具有任意Dilaton势的Jackiw-Teitelboim（JT）重力的引力扰动，并研究可将二次作用视为 $Ť\overline{Ť}$-物质动作变形。作为一种特殊情况，Dubovsky等人讨论了平面空间JT重力。包含[arXiv：1706.06604]。另一个有趣的例子是双曲型扩张势。这种情况相当于宇宙常数为负的经典Liouville引力，然后$Ť\overline{Ť}$具有有限耦合的物质作用的形变被实现为对AdS ₂的重力摄动。