https://doi.org/10.1140/epjc/s10052-016-4555-1
Regular Article - Theoretical Physics
Holographic free energy and thermodynamic geometry
1
S.N. Bose National Centre for Basic Sciences, JD Block, Sector III, Salt Lake, Kolkata, 700098, India
2
Indian Institute of Science Education and Research, Kolkata, Mohanpur, Nadia, 741246, India
3
Department of Physics, West Bengal State University, Barasat, 700126, India
4
Inter University Centre for Astronomy and Astrophysics, Pune, 411007, India
* e-mail: sunandan.gangopadhyay@gmail.com
** e-mail: sunandan@iiserkol.ac.in
*** e-mail: sunandan@associates.iucaa.in
Received:
1
October
2016
Accepted:
5
December
2016
Published online:
21
December
2016
We obtain the free energy and thermodynamic geometry of holographic superconductors in 
dimensions. The gravitational theory in the bulk dual to this -dimensional strongly coupled theory lives in the 
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 in the probe limit approximation which neglects the back reaction of the matter fields on the background spacetime geometry. 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.
© The Author(s), 2016
