Gravity/CMT Holography and Non-linear Electrodynamics

The aim of this thesis is the study of a holographic description of condensed matter systems by means of the anti-de Sitter/conformal field theory (AdS/CFT) correspondence which involves models of non-linear electrodynamics. After exposing the main concepts of AdS/CFT and generic non-linear electrodynamics, we study effects of the recently found (non-linear) ModMax electrodynamics on the minimal holographic superconductor in the background of a Schwarzschild-AdS black hole spacetime, and compare the results with the case of Maxwell electrodynamics. This is done by introducing in the background spacetime a charged scalar field minimally coupled to the ModMax electromagnetic field, and by using the correspondence to compute the behaviour of the dual scalar operator in the field theory, whose expectation value is identified with the order parameter, distinguish between the normal and superconducting state. We find that the scalar operator acquires a non-zero vacuum expectation value below a critical temperature and the effect of ModMax is to enhance its value. The critical temperature at which this happens and the optical conductivity of the field theory are unaffected by the introduction of ModMax. We also analyze the effect of ModMax on the Reissner-Nordström AdS planar black hole since it represents the main ingredient for dualizing finite density boundary theories.