On time-dependent AdS/CFT

TL;DR

This paper clarifies key aspects of Lorentzian AdS/CFT, deriving bulk-to-boundary propagators and boundary conditions, and connecting bulk methods to boundary field theory formalisms for time-dependent phenomena.

Contribution

It provides a detailed derivation of propagators and boundary conditions in Lorentzian AdS/CFT, enhancing understanding of time-dependent holographic dualities.

Findings

Derived bulk-to-boundary propagators for advanced, retarded, and Feynman functions.

Clarified boundary conditions at the horizon for bulk fields.

Connected bulk methods to the closed time path formalism in boundary theory.

Abstract

We clarify aspects of the holographic AdS/CFT correspondence that are typical of Lorentzian signature, to lay the foundation for a treatment of time-dependent gravity and conformal field theory phenomena. We provide a derivation of bulk-to-boundary propagators associated to advanced, retarded and Feynman bulk propagators, and provide a better understanding of the boundary conditions satisfied by the bulk fields at the horizon. We interpret the subleading behavior of the wavefunctions in terms of specific vacuum expectation values, and compute two-point functions in our framework. We connect our bulk methods to the closed time path formalism in the boundary field theory.