Brane effective actions and their island rule from TT̅ flows
Abstract
We derive a 2d effective action for semi-classical AdS3 gravity with an EOW brane of arbitrary tension by solving the radial Hamiltonian flow in a derivative expansion. Interpreting the radial flow as an RG flow, the effective theory is identified with a TT̅-like deformed CFT. This leads us to propose that the holographic dual for semi-classical AdS3 gravity with Neumann or conformal boundary conditions is obtained by setting the TT̅-like deformed CFT free. We verify our proposal explicitly for saddles corresponding to (A)dS2 branes in empty AdS3. We discuss three useful ways to decompose the effective brane theory into a matter sector (TT̅-deformed, TT̅-like deformed, and undeformed CFT, respectively) and a corresponding braneworld gravity sector. In particular, the split into TT̅-deformed CFT coupled to TT̅-like deformed Liouville gravity directly extends the Liouville description of the integrated Weyl anomaly into the bulk. The effective action is then used to perform an island-rule calculation for a non-asymptotic brane in an AdS/bCFT set-up, finding exact agreement with the Ryu-Takayanagi result. This extends previous holographic checks on the island rule to non-asymptotic regimes of application, as well as provides a Wald entropy interpretation for TT̅ entanglement. Finally, we relate our effective theory and its higher derivative corrections to AdS3 gravity with a fluctuating radial cutoff by explicit calculation of the on-shell action.
Related
- Brane flows
- Schwinger-Keldysh effective actions for non-hydrodynamic poles and branch cuts
- A stationary composition law for Schwinger-Keldysh effective actions
- Anomaly effective actions for 4d 𝒩=1 superconformal field theories
- Topology of Hawking-Page phase transition and equilibrium phases in AdS brane backgrounds
BibTeX
@misc{callebaut2026brane,
title = {{Brane effective actions and their island rule from $T\overline T$ flows}},
author = {Nele Callebaut and Matteo Selle},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.30533},
eprint = {2608.30533},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30533},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Brane effective actions and their island rule from TT̅ flows
AU - Nele Callebaut
AU - Matteo Selle
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.30533
UR - https://arxiv.org/abs/2608.30533
AB - We derive a 2d effective action for semi-classical AdS_3 gravity with an EOW brane of arbitrary tension by solving the radial Hamiltonian flow in a derivative expansion. Interpreting the radial flow as an RG flow, the effective theory is identified with a TT̅-like deformed CFT. This leads us to propose that the holographic dual for semi-classical AdS_3 gravity with Neumann or conformal boundary conditions is obtained by setting the TT̅-like deformed CFT free. We verify our proposal explicitly for saddles corresponding to (A)dS_2 branes in empty AdS_3. We discuss three useful ways to decompose the effective brane theory into a matter sector (TT̅-deformed, TT̅-like deformed, and undeformed CFT, respectively) and a corresponding braneworld gravity sector. In particular, the split into TT̅-deformed CFT coupled to TT̅-like deformed Liouville gravity directly extends the Liouville description of the integrated Weyl anomaly into the bulk. The effective action is then used to perform an island-rule calculation for a non-asymptotic brane in an AdS/bCFT set-up, finding exact agreement with the Ryu-Takayanagi result. This extends previous holographic checks on the island rule to non-asymptotic regimes of application, as well as provides a Wald entropy interpretation for TT̅ entanglement. Finally, we relate our effective theory and its higher derivative corrections to AdS_3 gravity with a fluctuating radial cutoff by explicit calculation of the on-shell action.
ER -