TY - JOUR

T1 - Free energy of a Lovelock holographic superconductor

AU - Aranguiz, Ligeia

AU - Miskovic, Olivera

N1 - Funding Information:
The authors thank Rodrigo Olea and Dumitru Astefanesei for useful comments. L.A. would also like to thank Stefan Theisen for hospitality during her stay at Max Planck Institute for Gravitational Physics (Albert Einstein Institute). This work was supported by Chilean FONDECYT grant Nb.1110102. O.M. is grateful to DII-PUCV for their support through the project Nb.123.711/2011. The work of L.A. is financed in part by Chilean grants NAC-doctorado Nb.21090754, BCH-pasantia doctoral Nb.75120006, and the UTFSM projects PIIC/2011-2013.
Publisher Copyright:
© 2014, The Author(s).

PY - 2014/8/1

Y1 - 2014/8/1

N2 - 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 high-temperature 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.

AB - 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 high-temperature 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.

UR - http://www.scopus.com/inward/record.url?scp=84905310389&partnerID=8YFLogxK

U2 - 10.1140/epjc/s10052-014-2975-3

DO - 10.1140/epjc/s10052-014-2975-3

M3 - Article

AN - SCOPUS:84905310389

VL - 74

SP - 1

EP - 19

JO - European Physical Journal C

JF - European Physical Journal C

SN - 1434-6044

IS - 8

M1 - 2975

ER -