One-dimensional backreacting holographic p-wave superconductors

We analytically and numerically study the properties of one-dimensional holographic p-wave superconductors in the presence of backreaction. We employ the Sturm-Liouville eigenvalue problem for the analytical calculation and the shooting method for the numerical investigations. We apply the AdS(3)/CFT2 correspondence and determine the relation between the critical temperature T-c and the chemical potential mu for different values of the mass m of a charged spin-1 field rho(mu) and backreacting parameters. We observe that the data of both analytical and numerical studies are in good agreement. We find that increasing the backreaction and the mass parameter causes the greater values for T-c/mu. Thus, it makes the condensation harder to form. In addition, the analytical and numerical approaches show that the value of the critical exponent beta is 1/2, which is the same as in the mean field theory. Moreover, both methods confirm the existence of a second order phase transition.