Anomaly Induced Current in Boundary Lifshitz Field Theory

Abstract: We study quantum transport phenomena induced by anisotropic Lifshitz scale anomaly in a boundary Lifshitz field theory (BLFT) coupled to an external electromagnetic background. In this context, we obtain the anisotropic scale anomaly in Lifshitz field theories coupled to a background $U(1)$ gauge field and subsequently compute the anomaly induced near boundary current in a BLFT. Focusing on 5D BLFTs, we find that the temporal and spatial components of the induced current exhibit distinct power law dependencies on the distance from the boundary, reflecting the intrinsic time-space anisotropy of the theory. We further derive this anomalous current holographically from the bulk dual of BLFT and find that the temporal component is independent of the boundary conditions while the spatial component depends explicitly on them. The distance dependence is in exact agreement with the dual field theory result.