Holographic P-wave Superconductors in 1+1 Dimensions

OpenAlex lv

We study ($1+1$)-dimensional $P$-wave holographic superconductors described by three- dimensional Einstein-Maxwell gravity coupled to a massive complex vector field in the context of ${\mathrm{AdS}}_{3}/{\mathrm{CFT}}_{2}$ correspondence. In the probe limit, where the backreaction of matter fields is neglected, we show that there is a formation of a vector hair around the black hole below a certain critical temperature. In the dual strongly coupled ($1+1$)-dimensional boundary theory, this holographically corresponds to the formation of a charged vector condensate which breaks spontaneously both the $U(1)$ and $SO(1,1)$ symmetries. We numerically compute both the free energy and the ac conductivity for the superconducting phase of the boundary field theory. Our numerical computations clearly establish that the superconducting phase of the boundary theory is favorable to the normal phase, and the presence of a magnetic moment term in the dual bulk theory effects the conductivity in the boundary field theory.