Novel Solutions of Finite-Density D3/D5 Probe Brane System and Their Implications for Stability

In this article we present a novel set of solutions of the probe brane system consisting of Nf-D5 probe branes embedded in the near-horizon geometry generated by Nc-D3 branes, with the D5 worldvolume U(1) gauge fields turned on. Our system is holographically dual to a supersymmetric defect field theory at finite density in non-trivial vacua. We find that a large class of vacua turns out to satisfy a no-force condition, even with supersymmetry explicitly broken by the finite density; our solutions include configuration in which charge separates from the horizon and is instead carried by probe branes outside the horizon. The free energy is lowered in this process. Whether this corresponds to a genuine instability of the finite-density probe brane system remains to be seen.