Würzburg Seminar on Quantum Field Theory and Gravity

In this talk, based on my recent paper hep-th/2510.01099, I will discuss the holographic interpretation of braneworld theories (AdS gravity with Neumann boundary conditions at finite cutoff), which in the last years have gained renewed attention in the context of the black hole information paradox due to their role in the formulation of the island rule for entanglement entropy. I will begin by revisiting the original dictionary for braneworld holography, identifying the so-called "cutoff CFT" with a T^2 deformed CFT. The boundary dual is thus given by a T^2-deformed CFT that is set free, i.e. coupled to the effective braneworld gravity. After discussing the refined dictionary for general bulk dimensions, I will focus on the case of a 3-dimensional bulk. In this context, I will argue that the 2-dimensional braneworld gravity is sourced by the Weyl behaviour of the dual boundary theory. Under suitable assumptions, we find that the braneworld gravity is given by a T\bar{T}-like deformed timelike Liouville theory that provides a bulk extension of the integrated Weyl anomaly of the holographic CFT.