Causal structures and holography

TL;DR

This paper investigates how bulk causal structures are represented in dual field theories, revealing modifications in the micro-causal light cone for non-commutative theories and establishing a correspondence with bulk spacetime properties.

Contribution

It introduces a detailed analysis of causal structures in dual field theories with spacelike and lightlike non-commutativity, linking them to modifications in bulk spacetime causality.

Findings

Boundary causal structure is asymptotically modified in non-commutative theories.

The micro-causal light cone in the dual field theory matches bulk predictions.

Spacetimes with lightlike non-commutativity are non-distinguishing, lacking closed causal curves.

Abstract

We explore the description of bulk causal structure in a dual field theory. We observe that in the spacetime dual to a spacelike non-commutative field theory, the causal structure in the boundary directions is modified asymptotically. We propose that this modification is described in the dual theory by a modification of the micro-causal light cone. Previous studies of this micro-causal light cone for spacelike non-commutativite field theories agree with the expectations from the bulk spacetime. We describe the spacetime dual to field theories with lightlike non-commutativity, and show that they generically have a drastic modification of the light cone in the bulk: the spacetime is non-distinguishing. This means that the spacetime while being devoid of closed timelike or null curves, has causal curves that are ``almost closed''. We go on to show that the micro-causal light cone in the field theory agrees with this prediction from the bulk.