Holographic superconductors and black holes

Abstract

The AdS/CFT correspondence relates a gravitational theory in AdS_{d+1} to a conformal field theory on its flat d-dimensional boundary, and a quasi-phenomenological approach was used to apply it to condensed matter systems. One application involves the holographic superconductivity. In order to describe a superconductor one needs a notion of temperature and a condensate. On the gravity side, these properties are achieved with the introduction of black holes with non-trivial scalar hair, which present also interesting transport properties. We plan to study such duality for the massive ABJM model, its transport properties, and explore the possible modifications of the gravity dual models. We plan to study the effect of the abelian reduction of the ABJM model on its gravity dual, as well as the relation between the resulting LG model and the original ABJM model. Also, the horizon of AdS_4 black holes can be mapped to a fluid, and one can study this correspondence for the case of the duality to the ABJM model.