Geometrizing $$ T\overline{T} $$

A bstract The $$ T\overline{T} T ¯ deformation can be formulated as a dynamical change of coordinates. We establish and generalize this relation to curved spaces by coupling the undeformed theory 2d gravity. For space coordinates is supplemented Weyl transformation. also sharpen holographic correspondence cutoff AdS 3 in multiple ways. First, we show that action annular region between surface boundary given precisely operator integrated over either or asymptotic boundary. Then derive coordinate transformations directly from bulk. Finally, reproduce flow equation for deformed stress tensor geometry.