Transport Properties of Holographic Defects

TL;DR

This work investigates charge transport on a (2+1)-dimensional defect in a strongly coupled (3+1)-dimensional N=4 SYM plasma using AdS/CFT with probe D5- and D7-branes. By computing defect current correlators in linear response, it reveals a conduction threshold set by the wave-number and shows that the transport properties are largely universal between the D5 and D7 realizations, despite differing supersymmetry. The analysis uncovers a rich structure: a diffusion-dominated hydrodynamic regime, a collisionless regime with a quasiparticle tower governed by an effective width of the defect, and a finite-$\lambda$ correction that breaks electromagnetic duality and induces frequency dependence in the conductivity. The presence of an internal flux introduces a tunable scale $f$ that controls resonance spacing, the effective temperature $T_{\mathrm{eff}}$, and the diffusion constant, linking holographic defect dynamics to emergent width-like effects. Additionally, a topological $\theta$-term yields a quantized Hall response, illustrating how holographic defect CFTs encode both dissipative and topological transport phenomena with implications for strongly correlated systems.

Abstract

We study the charge transport properties of fields confined to a (2+1)-dimensional defect coupled to (3+1)-dimensional super-Yang-Mills at large-$\nc$ and strong coupling, using AdS/CFT techniques applied to linear response theory. The dual system is described by $\nf$ probe D5- or D7-branes in the gravitational background of $\nc$ black D3-branes. Surprisingly, the transport properties of both defect CFT's are essentially identical -- even though the D7-brane construction breaks all supersymmetries. We find that the system possesses a conduction threshold given by the wave-number of the perturbation and that the charge transport arises from a quasiparticle spectrum which is consistent with an intuitive picture where the defect acquires a finite width. We also examine finite-$λ$ modifications arising from higher derivative interactions in the probe brane action.