Holographic complexity and noncommutative gauge theory

  • Josiah Couch
  • Stefan Eccles
  • Willy Fischler
  • Ming-Lei Xiao
Open Access
Regular Article - Theoretical Physics


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 Dp branes and also turn on the B field. Multiple noncommutative directions are considered in higher p cases.


AdS-CFT Correspondence Gauge-gravity correspondence 


Open Access

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Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Theory Group, Department of Physics and Texas Cosmology CenterThe University of Texas at AustinAustinU.S.A.

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