A supersymmetric color superconductor from holography

Abstract

Abstract We use holography to study d = 4, $$ \mathcal{N}=4 $$ N = 4 , SU(N c) super Yang-Mills coupled to N f ≪ N c quark flavors. We place the theory at finite isospin density n I by turning on an isospin chemical potential μ I = M q, with M 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 f D7-brane probes in AdS5 × S5. 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 I ≪ μ 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.