Toward a Holographic Model of Superconducting Fermions
arXiv:0811.0198 · doi:10.1088/1126-6708/2009/01/074
Abstract
We use the AdS/CFT correspondence to study N=4 supersymmetric SU(Nc) Yang-Mills theory, in the limits of large Nc and large 't Hooft coupling, coupled to a number Nf of massless hypermultiplet fields in the fundamental representation of the gauge group. We identify a U(1) subgroup of the R-symmetry under which the fermions in the hypermultiplet are charged but the scalars are not. All the hypermultiplet fields are also charged under a U(1) baryon number symmetry. We introduce an external magnetic field for the baryon number U(1), which triggers the spontaneous breaking of the U(1) R-symmetry, and we then introduce a chemical potential for the U(1) R-charge, producing a state with a nonzero density of the U(1) R-charge. The system should then exhibit superconductivity of the U(1) R-charge. The dual supergravity description is a number Nf of D7-branes in AdS5 x S5 with angular momentum on the S5 and a worldvolume magnetic field. We study the zero-temperature thermodynamics of the system, and find that for sufficiently large magnetic field the system prefers to be in the symmetry-broken phase. For smaller magnetic fields we find a discontinuous free energy, indicating that our gravitational setup does not capture all equilibrium states of the field theory.
arXiv comment32 pages, 22 eps files in 9 figures
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