Free energy of a Lovelock holographic superconductor

Abstract

We study thermodynamics of black hole solutions in Lanczos-Lovelock anti-de Sitter gravity in d + 1 dimensions coupled to nonlinear electrodynamics and a Stückelberg scalar field. This class of theories is used in the context of gauge/gravity duality to describe a hightemperature superconductor in d dimensions. A larger number of coupling constants in the gravitational side is necessary to widen the domain of validity of physical quantities in dual quantum field theory (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 we obtain the exact formula for the free energy of the superconductor in the holographic QFT. 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.

Relativistic strange quark stars in Lovelock gravity

“…In more than four dimensions higher order curvature terms are natural in Lovelock theory [6], and also higher order curvature corrections appear in the low-energy effective equations of Superstring Theory [7].The amount of published works in the literature reveals that Lovelock gravity is an exciting and active field. Black hole physics [8][9][10][11][12][13][14], cosmological solutions [15][16][17][18] and holographic superconductors exploiting the gauge/gravity duality [19] are some of the areas that have been explored in the framework of Lovelock gravity. However, the astrophysical implications of Lovelock theory should also be investigated.…”

Lovelock gravities from Born–Infeld gravity theory

“…Those symmetries were introduced in Refs.c [28,29,30,31,32,33,34] and can be regarded as generalizations of the so called Maxwell algebra [35,36], which describes the symmetries of quantum fields in Minkowski space with the presence of a constant electromagnetic field. Thus, for completeness and also due to the growing interest in the effect of higher-curvature terms in the holographic context (see for example [37,38,39,40]), in this work we will show that different Lovelock gravity actions in even dimensions can be obtained from a BI action based on the C m algebra. We shall start by considering the six-dimensional spacetime since it allows us to obtain a bigger variety of gravity theories.…”

Topological black holes in pure Gauss-Bonnet gravity and phase transitions

“…Thus, higher-curvature interaction in pure Lovelock gravity is also expected to show new features in a dual field theory. It has already been observed that there are holographic s-wave [27] and p-wave [28,29] phase transitions in a superconductor dual to higher-order gravity, such as Einstein-Gauss-Bonnet superconductor [30,31,32], and the field theories dual to quasitopological gravity [33,34], as well as Lovelock gravity [35,36]. Numerous work on this topic confirms that higher-order terms indeed have a notable effect on phase transitions, as they modify previously universal behavior of holographic theories.…”

“…Another important difference with respect to the backreaction noted in Ref. [35], is that the action needs scalar field counterterms when evaluated in the probe limit, since it becomes IR divergent. This counterterm is discussed in Ref.…”