Flavored anisotropic black holes

Abstract

We construct a black hole geometry dual to a (2+1)-dimensional defect in an ambient (3+1)-dimensional gauge theory at non-zero temperature and quark density. The geometry is a solution to the equations of motion of type IIB supergravity with brane sources, a low energy limit of an intersection of stacks of color D3-branes and flavor D5-branes. We consider the case in which the number of D5-branes is large and they can be homogeneously distributed along the directions orthogonal to the defect, creating in this way a multilayer structure. The quark density is generated by exciting a gauge field in the worldvolume of the dynamic brane sources. We study the thermodynamics of the anisotropic black hole and compute the energy density of the dual theory, as well as the pressures and speeds of sound along the directions parallel and orthogonal to the defect. We also calculate transport coefficients in the shear channel, quark-antiquark potentials, and the entanglement entropies for slab subregions. These analyses give us a good overview on how the degrees of freedom are spread, entangled, and behave in this unquenched system in the deconfining phase at strong coupling.