Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Diffusion constant of slowly rotating black three-brane   In this paper, we take the slowly rotating black three-brane background and
perturb it by introducing a vector gauge field. We find the components of the
gauge field through Maxwell equations and Bianchi identities. Using currents
and some ansatz we find Fick's first law at long wavelength regime. An
interesting result for this non-trivial supergravity background is that the
diffusion constant on the stretched horizon which emerges from Fick's first law
is a complex constant. The pure imaginary part of the diffusion constant
appears because the black three-brane has angular momentum. By taking the
static limit of the corresponding black brane the well known diffusion constant
will be recovered. On the other hand, from the point of view of the Fick's
second law, we have the dispersion relation $\omega=-iDq^{2}$ and we found a
damping of hydrodynamical flow in the holographically dual theory. Existence of
imaginary term in the diffusion constant introduces an oscillating propagation
of the gauge field in the dual field theory.

8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
2
The categories of this paper are: math
3
The categories of this paper are: physics