A Supersymmetric Color Superconductor from Holography

We use holography to study $d=4$, $\mathcal{N}=4$, SU($N_{\rm \tiny{c}}$) super Yang-Mills coupled to $N_{\rm \tiny{F}} \ll N_{\rm \tiny{c}}$ quark flavors. We place the theory at finite isospin density $n_{\rm \tiny{I}}$ by turning on an isospin chemical potential $\mu_{\rm \tiny{I}}=M_{\rm \tiny{q}}$, with $M_{\rm \tiny{q}}$ the quark mass. We also turn on two R-symmetry charge densities $n_1=n_2$. We show that the ground state is a supersymmetric, superfluid, color superconductor, namely a finite-density state that preserves a fraction of supersymmetry in which part of the global symmetries and part of the gauge symmetries are spontaneously broken. The holographic description consists of $N_{\rm \tiny{F}}$ D7-brane probes in $\mbox{AdS}_5 \times \mbox{S}^5$. The symmetry breaking is due to the dissolution of some D3-branes inside the D7-branes triggered by the electric field associated to the isospin charge. The massless spectrum contains Goldstone bosons and their fermionic superpartners. The massive spectrum contains long-lived, mesonic quasi-particles if $n_{\rm \tiny{I}} \ll \mu_{\rm \tiny{I}}^3$, and no quasi-particles otherwise. We discuss the possibility that, despite the presence of mass scales and charge densities in the theory, conformal and relativistic invariance arise as emergent symmetries in the infrared.
Comment: 11 pages, 2 figures. v2: comments and references added, published text