Brane dynamics from the first law of entanglement

TL;DR

This paper derives the linearized equations of motion for brane-world models in warped AdS spacetimes from the first law of entanglement, connecting boundary BCFT constraints with bulk gravity equations.

Contribution

It demonstrates how the first law of entanglement leads to local linearized equations of motion for branes in warped AdS, extending previous results to more general covariant bulk theories.

Findings

Derived boundary constraints from the first law of entanglement.

Established the Neumann boundary condition as a consequence of entanglement considerations.

Outlined a path to generalize to higher-derivative gravity theories.

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.