Holographic Complexity in Non-commutative Field Theory

I will talk about the holographic complexity of a non-commutative field theory. The four-dimensional N=4 non-commutative 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 field. I start from this example and found 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 bound which is exactly 1/4 larger than the commutative value. The finite time behavior of the complexity implies that the new bound may be a better candidate for the Lloyd bound of complexity growth rate, compared to the commutative Schwarzschild black hole. We then attempt to explain the enhancement based on some quantum mechanics intuition. 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 non-commutative directions are considered in higher p cases.