Relating chronology protection and unitarity through holography

TL;DR

This paper demonstrates that in a holographic setting, violations of unitarity in the dual CFT correspond to the formation of closed timelike curves in the bulk, providing a holographic argument for chronology protection.

Contribution

It presents a simple nonsupersymmetric example linking chronology protection to unitarity via AdS/CFT correspondence, with explicit geometry and dual CFT analysis.

Findings

Chronology violation occurs when the dust ball exceeds a critical radius.

Unitarity bound violation in the dual CFT coincides with the appearance of closed timelike curves.

Holographic duality enforces chronology protection through unitarity constraints.

Abstract

We give a simple nonsupersymmetric example in which chronology protection follows from unitarity and the AdS/CFT correspondence. We consider a ball of homogeneous, rotating dust in global AdS3 whose backreaction produces a region of Goedel space inside the ball. We solve the Israel matching conditions to find the geometry outside of the dust ball and compute its quantum numbers in the dual CFT. When the radius of the dust ball exceeds a certain critical value, the spacetime will contain closed timelike curves. Our main observation is that precisely when this critical radius is exceeded, a unitarity bound in the dual CFT is violated, leading to a holographic argument for chronology protection.