Chaos and entanglement spreading in a non-commutative gauge theory

TL;DR

This paper investigates how non-local interactions in a non-commutative gauge theory influence quantum information spread, revealing that non-locality can increase velocities of chaos propagation beyond traditional bounds.

Contribution

It demonstrates that non-commutative geometry enhances butterfly and entanglement velocities, challenging existing bounds on quantum information spread in local theories.

Findings

Butterfly velocity increases with non-commutativity.

Entanglement velocity increases with non-commutativity.

Scrambling time and Lyapunov exponent remain unaffected.

Abstract

Holographic theories with classical gravity duals are maximally chaotic: they saturate a set of bounds on the spread of quantum information. In this paper we question whether non-locality can affect such bounds. Specifically, we consider the gravity dual of a prototypical theory with non-local interactions, namely, $\mathcal{N}=4$ non-commutative super Yang Mills. We construct shock waves geometries that correspond to perturbations of the thermofield double state with definite momentum and study several chaos related properties of the theory, including the butterfly velocity, the entanglement velocity, the scrambling time and the maximal Lyapunov exponent. The latter two are unaffected by the non-commutative parameter $\theta$, however, both the butterfly and entanglement velocities increase with the strength of the non-commutativity. This implies that non-local interactions can enhance the effective light-cone for the transfer of quantum information, eluding previously conjectured bounds encountered in the context of local quantum field theory. We comment on a possible limitation on the retrieval of quantum information imposed by non-locality.