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arXiv · 1710.07833

Holographic complexity and non-commutative gauge theory

Josiah Couch·Stefan Eccles·Willy Fischler·Ming-Lei Xiao
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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.

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Josiah Couch, Stefan Eccles, Willy Fischler, Ming-Lei Xiao. 2018-03-20. Holographic complexity and non-commutative gauge theory. https://doi.org/10.1007/jhep03(2018)108

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