Modular Hamiltonian for holographic excited states

Abstract

In this work we study the Tomita-Takesaki construction for a family of excited states that, in a strongly coupled CFT—at large N—correspond to coherent states in an asymptotically AdS spacetime geometry. We compute the modular flow and modular Hamiltonian associated to these excited states in the Rindler wedge and for a ball shaped entangling surface. Using holography, one can compute the bulk modular flow and construct the Tomita-Takesaki theory for these cases. We also discuss generalizations of the entanglement regions in the bulk and how to evaluate the modular Hamiltonian in a large N approximation. Finally, we extend the holographic Banks, Douglas, Horowitz and Matinec (BDHM) formula to compute the modular evolution of operators in the corresponding CFT algebra, and propose this as a more general prescription.