Chern–Simons superconductor

We study the effect of a bulk Chern–Simons (CS) term on a (3+1) dimensional type II superconductor in the context of the AdS/CFT correspondence. We holographically compute the supercurrent and find that it is nonlocal in nature. It receives nontrivial corrections due to the presence of the CS term. Considering a large limit of a parameter λ (we call this limit the long wavelength limit), which is effectively the high temperature limit of the theory, we find that this nonlocal supercurrent boils down to a local quantity. The leading term (without the CS term) of this current matches the result of the Ginzburg–Landau (GL) theory. We compute the effect of the CS term on the GL current and find that the effect is greatly suppressed at high temperature ((1/(T⁴))). Finally, the free energy of the vortex configuration has been calculated. The free energy also receives nontrivial correction on the order of 1/λ² in the long wavelength approximation. (paper)