Time singularities of correlators from Dirichlet conditions in AdS/CFT

TL;DR

This paper develops a method to analyze the leading singularities of two-point correlators in AdS/CFT with Dirichlet boundary conditions, revealing new boundary-related singularities and their possible interpretation as non-local deformations.

Contribution

It introduces a general procedure for determining correlator singularities in AdS/CFT with Dirichlet conditions, highlighting new boundary-induced singularities and their field theory interpretation.

Findings

New singularities at boundary points connected by null geodesics.

Dirichlet conditions influence the correlator's singularity structure.

Proposed interpretation as non-local double trace deformation.

Abstract

Within AdS/CFT, we establish a general procedure for obtaining the leading singularity of two-point correlators involving operator insertions at different times. The procedure obtained is applied to operators dual to a scalar field which satisfies Dirichlet boundary conditions on an arbitrary time-like surface in the bulk. We determine how the Dirichlet boundary conditions influence the singularity structure of the field theory correlation functions. New singularities appear at boundary points connected by null geodesics bouncing between the Dirichlet surface and the boundary. We propose that their appearance can be interpreted as due to a non-local double trace deformation of the dual field theory, in which the two insertions of the operator are separated in time. The procedure developed in this paper provides a technical tool which may prove useful in view of describing holographic thermalization using gravitational collapse in AdS space.