Holographic free energy and thermodynamic geometry

Abstract

We analytically obtain the free energy and thermodynamic geometry of holographic superconductors in $2+1$-dimensions. The gravitational theory in the bulk dual to this $2+1$-dimensional strongly coupled theory lives in the $3+1$-dimensions and is that of a charged $AdS$ black hole together with a massive charged scalar field. The matching method is applied to obtain the nature of the fields near the horizon using which the holographic free energy is computed through the gauge/gravity duality. The critical temperature is obtained for a set of values of the matching point of the near horizon and the boundary behaviour of the fields. The thermodynamic geometry is then computed from the free energy of the boundary theory. From the divergence of the thermodynamic scalar curvature, the critical temperature is obtained once again. We then compare this result for the critical temperature with that obtained from the matching method.

13 pages Latex

References in corpus (6)

• Building an AdS/CFT superconductor
• Lectures on Holographic Superfluidity and Superconductivity
• Holographic Superconductors with Various Condensates
• A Non-Fermi Liquid from a Charged Black Hole; A Critical Fermi Ball
• An Analytic Holographic Superconductor
• Analytical Studies on Holographic Insulator/Superconductor Phase Transitions

Cited by in corpus (2)

• Holographic insulator/superconductor phase transition in higher dimensional Gauss-Bonnet gravity
• Effects of massive gravity on $s$-wave holographic superconductor