Holographic complexity and noncommutative gauge theory
Abstract
We study the holographic complexity of noncommutative field theories. The fourdimensional N=4 noncommutative super YangMills 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 nontrivial NSNS 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 noncommutativity 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 nontrivial 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.
 Publication:

Journal of High Energy Physics
 Pub Date:
 March 2018
 DOI:
 10.1007/JHEP03(2018)108
 arXiv:
 arXiv:1710.07833
 Bibcode:
 2018JHEP...03..108C
 Keywords:

 AdSCFT Correspondence;
 Gaugegravity correspondence;
 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 JHEP 2018 (2018) 108