Holographic complexity and non-commutative gauge theory

TL;DR

This paper investigates how noncommutative gauge theories affect holographic complexity, revealing an enhancement in the late-time complexity growth rate due to noncommutativity, with potential quantum explanations and extensions to various string theory setups.

Contribution

It demonstrates that noncommutativity increases holographic complexity growth rate, providing a quantitative analysis and exploring extensions to multiple noncommutative directions in string theory.

Findings

Complexity growth rate is enhanced by noncommutativity.

The enhancement saturates at 1/4 larger than the commutative case.

Finite time complexity behavior is also analyzed.

Abstract

We study the holographic complexity of noncommutative field theories. The four-dimensional $\mathcal{N}=4$ noncommutative super Yang-Mills theory with Moyal algebra along two of the spatial directions has a well known holographic dual as a type IIB supergravity theory with a stack of D3 branes and non-trivial NS-NS B fields. We start from this example and find that the late time holographic complexity growth rate, based on the "complexity equals action" conjecture, experiences an enhancement when the non-commutativity is turned on. This enhancement saturates a new limit which is exactly 1/4 larger than the commutative value. We then attempt to give a quantum mechanics explanation of the enhancement. Finite time behavior of the complexity growth rate is also studied. Inspired by the non-trivial result, we move on to more general setup in string theory where we have a stack of D$p$ branes and also turn on the B field. Multiple noncommutative directions are considered in higher $p$ cases.