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Infrared Behavior of Scalar Condensates in Effective Holographic Theories

We investigate the infrared behavior of the spectrum of scalar-dressed, asymptotically Anti de Sitter (AdS) black brane (BB) solutions of effective holographic models. These solutions describe scalar condensates in the dual field theories. We show that for zero charge density the ground state of these BBs must be degenerate with the AdS vacuum, must satisfy conformal boundary conditions for the scalar field and it is isolated from the continuous part of the spectrum. When a finite charge density is switched on, the ground state is not anymore isolated and the degeneracy is removed. Depending on the coupling functions, the new ground state may possibly be energetically preferred with respect to the extremal Reissner-Nordstrom AdS BB. We derive several properties of BBs near extremality and at finite temperature. As a check and illustration of our results we derive and discuss several analytic and numerical, BB solutions of Einstein-scalar-Maxwell AdS gravity with different coupling functions and different potentials. We also discuss how our results can be used for understanding holographic quantum critical points, in particular their stability and the associated quantum phase transitions leading to superconductivity or hyperscaling violation.