$T\bar{T}$ braneworld holography

We study a constructive gravitational dual of two-dimensional $T\bar{T}$-deformed conformal field theories (CFTs) grounded in their two-dimensional gravity description. This framework can be viewed as a Randall-Sundrum-type braneworld, where two-dimensional gravity localized on the $AdS_3$ boundary is dynamical. Assuming the AdS/CFT correspondence, the holographic dictionary provides a straightforward translation between the $T\bar{T}$-deformed CFT and its gravitational dual. In particular, this $T\bar{T}$ braneworld holography remains valid in the presence of matter. To clarify how our framework relates to -- and differs from -- the cutoff AdS proposal, we examine, in the absence of matter, the effect of dynamical boundary gravity on the bulk geometry. In general, semiclassical integration of the boundary two-dimensional gravity -- weighted by the massive gravity action -- leads to a deformation of the two-dimensional metric on constant-radial surfaces. However, we find that the surface commonly interpreted as the cutoff emerges dynamically as a characteristic bulk surface on which the deformation is neutralized. This perspective opens the door to possible extensions of our framework to incorporate matter effects on the bulk surface in future work.