Geometrizing TT

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

Automated summary

The TT deformation is formulated as a dynamical change of coordinates, generalized to curved spaces by coupling the undeformed theory to 2d gravity. The dynamical change of coordinates in curved space is supplemented by a dynamical Weyl transformation. The holographic correspondence to cutoff AdS(3) is sharpened by showing the action of the annular region can be given precisely by the TT operator integrated over either the cutoff surface or the asymptotic boundary, deriving dynamical coordinate and Weyl transformations directly from the bulk, and reproducing the flow equation for the deformed stress tensor from the cutoff geometry.