Glue-on AdS holography for $$ T\overline{T} $$-deformed CFTs

The $T\bar T$ deformation is a solvable irrelevant whose properties depend on the sign of parameter $\mu$. In particular, T$-deformed CFTs with $\mu<0$ have been proposed to be holographically dual Einstein gravity where metric satisfies Dirichlet boundary conditions at finite cutoff surface. this paper, we put forward holographic proposal for $\mu>0$, in which case bulk geometry constructed by gluing patch AdS$_3$ original spacetime. As evidence, show that trace flow equation, spectrum cylinder, and partition function torus sphere, among other results, can all reproduced from calculations glue-on AdS$_3$.