Brane dynamics from the first law of entanglement

Abstract

In this note, we study the first law of entanglement in a boundary conformal field theory (BCFT) dual to warped AdS cut off by a brane. Exploiting the symmetry of boundary-centered half-balls in the BCFT, and using Wald's covariant phase space formalism in the presence of boundaries, we derive constraints from the first law for a broad range of covariant bulk Lagrangians. We explicitly evaluate these constraints for Einstein gravity, and find a local equation on the brane which is precisely the Neumann condition of Takayanagi [arXiv:1105.5165] at linear order in metric perturbations. This is analogous to the derivation of Einstein's equations from the first law of entanglement entropy. This machinery should generalize to give local linearized equations of motion for higher-derivative bulk gravity with additional fields. arXiv:1912.05746v1 [hep-th]

Information transfer with a gravitating bath

“…Most work on islands in higher dimensions [9,[12][13][14][15][16][22][23][24][25][26], as well as some of the results in lower dimensions [27][28][29][30][31][32], have been obtained in the context of the Randall-Sundrum (RS) braneworlds [33] with subcritical tension branes [34,35], also known as the Karch-Randall (KR) braneworlds. Compared to the generic RS setup, KR has several specific features.…”

Information Transfer with a Gravitating Bath

“…Most work on islands in higher dimensions [8,[11][12][13][14][15][21][22][23][24][25], as well as some of the results in lower dimensions [26][27][28][29], have been obtained in the context of the Randall-Sundrum (RS) braneworlds [30] with subcritical tension branes [31,32], also known as the Karch-Randall (KR) braneworlds. Compared to the generic RS setup, KR has several specific features.…”