Abstract
We study thermodynamics of black hole solutions in Lanczos-Lovelock AdS gravity in d+1 dimensions coupled to nonlinear electrodynamics and a Stueckelberg scalar field. This class of theories is used in the context of gauge/gravity duality to describe a high-temperature superconductor in d dimensions. Larger number of coupling constants in the gravitational side is necessary to widen a domain of validity of physical quantities in a dual QFT. We regularize the gravitational action and find the finite conserved quantities for a planar black hole with scalar hair. Then we derive the quantum statistical relation in the Euclidean sector of the theory, and obtain the exact formula for the free energy of the superconductor in the holographic quantum field theory. Our result is analytic and it includes the effects of backreaction of the gravitational field. We further discuss on how this formula could be used to analyze second order phase transitions through the discontinuities of the free energy, in order to classify holographic superconductors in terms of the parameters in the theory.
Highlights
The proposal of Maldacena about an equivalence between the anti-de Sitter (AdS) gravity and the conformal field theory (CFT) in a smaller spacetime dimension [1,2,3,4] has brought to many successful applications of this correspondence to strongly coupled quantum systems
Motivated by an application of AdS/CFT correspondence to d-dimensional high-Tc superconductors that do not have a generally accepted theoretical model, we study the Stückelberg scalar field in (d + 1)-dimensional asymptotically AdS spacetime coupled to gravitational and electromagnetic fields
On the AdSd+1 gravity side, the black hole solution is associated to a thermal, dual QFTd and the scalar field couples to the order parameter of the superconductor in QFTd
Summary
The proposal of Maldacena about an equivalence between the anti-de Sitter (AdS) gravity and the conformal field theory (CFT) in a smaller spacetime dimension [1,2,3,4] has brought to many successful applications of this correspondence to strongly coupled quantum systems. A typical result is that the Gauss–Bonnet (GB) coupling decreases the critical temperature of the superconductor and makes the condensation harder [26,27,28,29,30,31] In these references, an analytical approach to the condensation in a holographic dual to EGB gravity that includes an effect of the backreaction of black holes in five dimensions was discussed. We are interested in analytic study of the effects of higher-order gravitational terms in AdS gravity and nonlinear electrodynamics on phase transitions in high-Tc holographic superconductors of the Stückelberg type, which includes the backreaction of the black holes. We shall focus on the first part of the above problem and only discuss the second part, which is work in progress
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