  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.

High Energy Physics - Theory;General Relativity and Quantum Cosmology