We show that a D3/D7 system (in the limit of zero quark mass) at finite isospin chemical potential goes through a superconductor (superfluid) like phase transition. This is similar to a flavored superfluid phase studied in the QCD literature, where mesonic operators condense. We have studied the frequency dependent conductivity of the condensate and found a delta function peak in the zero frequency limit. This is an example of superconductivity in a string theory context. Consequently we have found a superfluid/supercurrent type solution and studied the associated phase diagram. The superconducting transition changes from second order to first order at a critical superfluid velocity. We have studied various properties of the superconducting system like superfluid density, energy gap, second sound etc. We investigate the possibility of the isospin chemical potential modifying the embedding of the flavor branes by checking whether the transverse scalars also condense at low temperatures. This however does not seem to be the case.

Headrick and Takayanagi showed that the Ryu-Takayanagi holographic entanglement entropy formula generally obeys the strong subadditivity (SSA) inequality, a fundamental property of entropy. However, the Ryu-Takayanagi formula only applies when the bulk spacetime is static. It is not known whether the covariant generalization proposed by Hubeny, Rangamani, and Takayanagi (HRT) also obeys SSA. We investigate this question in three-dimensional AdS-Vaidya spacetimes, finding that SSA is obeyed as long as the bulk spacetime satisfies the null energy condition. This provides strong support for the validity of the HRT formula.

In this work we discuss the zero temperature limit of a "p-wave" holographic superconductor. The bulk description consists of a non-Abelian SU (2) gauge fields minimally coupled to gravity. We numerically construct the zero temperature solution which is the gravity dual of the superconducting ground state of the "p-wave" holographic superconductors. The solution is a smooth soliton with zero horizon size and shows an emergent conformal symmetry in the IR. We found the expected superconducting behavior. Using the near horizon analysis we show that the system has a "hard gap" for the relevant gauge field fluctuations. At zero temperature the real part of the conductivity is zero for an excitation frequency less than the gap frequency. This is in contrast with what has been observed in similar scalargravity-gauge systems (holographic superconductors). We also discuss the low but finite temperature behavior of our solution.

We model competition between different macroscopic orders in an holographic context. The orders we considered are a superconducting order, modeled by a charged scalar field, and a magnetic order modeled by a neutral scalar field. We also discuss the case of two competing scalars coupled to a single gauge field.In all cases discussed here the phases tend to compete, rather than enhance each other. The condensation of one scalar hinders any further instabilities, unless we have a sufficiently strong repulsive interactions between the bulk scalars. We provide both analytic arguments and numerical demonstration of this fact.Based on the cases discussed here, we conjecture that holographic orders tend to compete for attractive bulk interactions, including gravity, and to cooperate, or be mutually enhancing, for repulsive bulk interactions between the corresponding order parameters.

We study the region inside the event horizon of charged black holes in five dimensional asymptotically anti-de Sitter space, using as a probe two-sided correlators which are dominated by spacelike geodesics penetrating the horizon. The spacetimes we investigate include the Reissner-Nordström black hole and perturbations thereof. The perturbed spacetimes can be found exactly, enabling us to perform a local scan of the region between the inner and outer horizons. Surprisingly, the two-sided correlators we calculate seem to be geometrically protected from the instability of the inner horizon.