Holographic dual of a time machine

Abstract

Assuming that the AdS/CFT prescription is valid in the case of noncausal backgrounds, we apply it to the simplest possible eternal time machine solution in AdS 3 based on two conical defects moving around their center of mass along a circular orbit. Closed timelike curves in this space-time extend all the way to the boundary of AdS 3 , violating causality of the boundary field theory. By use of the geodesic approximation we address the issue of self-consistent dynamics of the dual 1 þ 1 dimensional field theory when causality is violated, and calculate the two-point retarded Green function. It has a nontrivial analytical structure both at negative and positive times, providing us with an intuition on how an interacting quantum field could behave once causality is broken.

Holographic instant conformal symmetry breaking by colliding conical defects

“…In the previous paper [1] we have studied deformations by massive moving particles in AdS 3 . Similar problems have been investigated in the early papers [2][3][4][5] for various models. For motivation to study these problems see [1] and references therein.…”

“…As the particle penetrates the bulk of AdS 3 deeper geodesics connecting the boundary points exhibit lensing effects. A similar effect takes place for massive particles [2][3][4][5], [1] and due to this effect one gets the zone structure for two-point correlators of the boundary theory. Considering collisions of two ultrarelativistic particles we get even more complicated structure for geodesics, that lead to a multi-zone structure for two-point correlators.…”

“…In papers [2][3][4][5], [1] the group theoretical language is used to describe the conical defects [6][7][8] by the corresponding cutting and gluing procedure. To calculate the two-point boundary correlators we use the geodesic approximation proposed in this context in [2].…”

Holographic dictionary and defects in the bulk

“…The latter leads to the fact that two given points in the bulk (or at the boundary) can be connected, generally speaking, by several geodesics. This has a crucial impact on the holographic dual of the AdS 3 with a point particle, as was shown in the recent work [21][22][23][24][25] based on the geodesic approximation [26]. The main object of study therein were two-point correlation functions and the entanglement entropy in the boundary dual to the AdS 3 -deficit spacetime in the framework of geodesic approximation.…”

“…The geodesic prescription for correlation functions [26] dual to particles (both static and moving) in AdS 3 has been constructed in [21][22][23][24][25]. It takes into account geodesics which wind around conical defects functions by including the contributions of image geodesics generated by the identification isometry.…”