Holographic dual of a time machine

TL;DR

This paper explores the holographic dual of a time machine in $AdS_3$, analyzing causality violations and quantum field behavior through geodesic approximation, revealing potential for consistent quantum evolution without extra constraints.

Contribution

It provides a holographic analysis of a time machine in $AdS_3$, demonstrating how causality violations affect the dual quantum field theory and showing possible consistent quantum evolution.

Findings

The retarded Green function exhibits complex analytical structure at positive and negative times.

Causality violations lead to non-trivial quantum field behavior in the dual theory.

Quantum evolution can be consistent without additional constraints despite causality breaking.

Abstract

We apply the $AdS/CFT$ holography 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 "grandfather paradox" in the dual $1+1$ dimensional field theory and calculate the two-point retarded Green function. It has a non-trivial 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. In contrast with the previous considerations our calculations reveal the possibility of a consistent and controllable evolution of a quantum system without any need to impose additional consistency constraints.