Modular Hamiltonian for holographic excited states

MARTINEZ, PEDRO J.; ARIAS, RAÚL; BOTTA-CANTCHEFF, MARCELO; ZARATE, JUAN F.

Physical Review D

APS Physics

Año: 2020 vol. 102

2470-0010

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.