Thermodynamic geometry of holographic superconductors

TL;DR

This paper explores the thermodynamic geometry of a strongly coupled (2+1)D quantum field theory at finite temperature using holography, linking phase transitions to scalar curvature in the bulk gravitational description.

Contribution

It analytically derives the thermodynamic metric and scalar curvature for a holographic superconductor, connecting geometric properties to phase transitions.

Findings

Thermodynamic scalar curvature signals the superconducting phase transition.

Analytical computation of holographic free energy in a (3+1)D charged AdS black hole.

Establishes a geometric characterization of phase transitions in holographic superconductors.

Abstract

We obtain the thermodynamic geometry of a (2+1) dimensional strongly coupled quantum field theory at a finite temperature in a holographic set up, through the gauge/gravity correspondence. The bulk dual gravitational theory is described by a (3+1) dimensional charged AdS black hole in the presence of a massive charged scalar field. The holographic free energy of the (2+1) dimensional strongly coupled boundary field theory is computed analytically through the bulk boundary correspondence. The thermodynamic metric and the corresponding scalar curvature is then obtained from the holographic free energy. The thermodynamic scalar curvature characterizes the superconducting phase transition of the boundary field theory.