Journal Article

Holographic complexity and noncommutative gauge theory

Eccles, Stefan, Couch, Josiah, Xiao, Ming-Lei, Fischler, Willy

2018

Overview

A bstract We study the holographic complexity of noncommutative field theories. The four-dimensional 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.

• Publisher: Springer Berlin Heidelberg,Springer Nature B.V,SpringerOpen
• Subject: AdS-CFT Correspondence / Branes / Classical and Quantum Gravitation / Commutativity / Complexity / Elementary Particles / Gauge theory / Gauge-gravity correspondence / Growth rate / High energy physics / Physics / Physics and Astronomy / Quantum Field Theories / Quantum Field Theory / Quantum mechanics / Quantum Physics / Quantum theory / Regular Article - Theoretical Physics / Relativity Theory / String Theory / Supergravity / Yang-Mills theory