Thermodynamic geometry of holographic superconductors

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