Anomaly induced transport in holographic superconductors

Abstract

We investigate the anomaly-induced transport properties of a holographic superconductor exhibiting spontaneous symmetry breaking. The holographic model incorporates vector and axial gauge fields, an additional non-anomalous $U(1)$ symmetry, and a charged scalar field that drives the phase transition. Working in the probe limit, we numerically construct the superconducting background under two alternative scalar field quantizations, corresponding to operators with scaling dimensions $Δ=1$ and $Δ=3$ (denoted as the $O_1$ and $O_2$ theories, respectively). Using Kubo formulae, we compute the chiral magnetic conductivities and examine their response to the scalar condensate. Our findings demonstrate that spontaneous symmetry breaking allows anomaly-induced transport to extend beyond anomalous currents, significantly impacting the non-anomalous sector as well. Remarkably, this effect appears in both theories, indicating that the influence on the non-anomalous sector is independent of the chosen quantization. The comparison of our numerical results with the analytical limits for $O_i \to 0$ and $O_i \to \infty$ $(i=1,2)$ reveals consistent behavior across both theories.