Holographic charge transport in non commutative gauge theories

Dibakar Roychowdhury

doi:10.1007/jhep07(2015)121

Abstract

In this paper, based on the holographic techniques, we explore the hydrodynamics of charge diffusion phenomena in non commutative $$ \mathcal{N}=4 $$ SYM plasma at strong coupling. In our analysis, we compute the R charge diffusion rates both along commutative as well as the non commutative coordinates of the brane. It turns out that unlike the case for the shear viscosity, the DC conductivity along the non commutative direction of the brane differs significantly from that of its cousin corresponding to the commutative direction of the brane. Such a discrepancy however smoothly goes away in the limit of the vanishing non commutativity.

Highlights

Even before these analysis had performed, in [30] the authors had studied hydrodynamics of a strongly coupled plasma in a slightly different context of anisotropy which was driven due to presence of the non commutativity along different spatial directions of the Dp brane in the presence of a background NS B field
In this paper, based on the holographic techniques, we explore the hydrodynamics of charge diffusion phenomena in non commutative N = 4 SYM plasma at strong coupling
In our analysis, considering the so called hydrodynamic limit, we explore the charge transport phenomena in non commutative N = 4 SYM plasma at strong coupling

Summary

The dual set up

We start our analysis with a formal introduction to the geometrical construction in the bulk space time that is holographically dual to non commutative N = 4 SYM theory at strong coupling. It is already known from the earlier literature that non commutative gauge theories at strong coupling could be consistently obtained from string theory by considering the so called decoupling limit in a system of Dp branes in the presence of a background NS B field that gives rise to certain scale of non commutativity in the large N limit [31]–[33]. From (2.2) it is quite trivial to note down the corresponding Hawking temperature which for the present case turns out to be, T

Charge diffusion

Charge susceptibility

Conductivity II: σ

Summary and final remarks