Abstract
Using gauge/gravity duality, we investigate charge localization near an inter-face in a strongly coupled system. For this purpose we consider a top-down holographic model and determine its conductivities. Our model corresponds to a holographic interface which localizes charge around a (1+1)-dimensional defect in a (2+1)-dimensional system. The setup consists of a D3/D5 intersection at finite temperature and charge density. We work in the probe limit, and consider massive embeddings of a D5-brane where the mass depends on one of the field theory spatial directions, with a profile interpolating between a negative and a positive value. We compute the conductivity in the direction parallel and perpendicular to the interface. For the latter case we are able to express the DC conductivity as a function of background horizon data. At the interface, the DC conductivity in the parallel direction is enhanced up to five times with respect to that in the orthogonal one. We study the implications of broken translation invariance for the AC and DC conductivities.
Highlights
Which are in general partial differential equations (PDEs)
To introducing translational symmetry breaking by spatially modulating the sources of conserved currents, momentum relaxation may be realized by explicitly breaking diffeomorphism invariance in the bulk [21,22,23,24,25,26,27], which in [28] led to progress on the study of the conductivity for systems with broken translational symmetry
The thermodynamic properties of the D7-brane model with a kink [36] were computed in [41], where the PDE equations of motion for the brane embedding in a black D3-brane background were solved, and the relationship between the charge density and the chemical potential was analyzed in connection with the possible fermionic character of the gapless interface excitations
Summary
We consider D3/D5 intersections at nonzero temperature and finite charge density, namely in the presence of a finite density of the fundamental matter dual to the open strings stretching between the D3- and D5-branes. The supersymmetric intersection of N D3- and Nf D5-branes along 2+1 spacetime dimensions is dual to (3+1)-dimensional N = 4 SYM with Nf fundamental hypermultiplets living on a (2+1)-dimensional defect [45, 46]. We work in the probe limit and at nonzero temperature, we treat the D5-branes as probes in the geometry generated by the black D3-branes
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