Anomaly Induced Current in Boundary Lifshitz Field Theory

TL;DR

This paper investigates how anisotropic Lifshitz scale anomalies induce boundary currents in Lifshitz field theories, revealing distinct power law behaviors and holographic duality insights.

Contribution

It introduces the first detailed analysis of anomaly-induced boundary currents in Lifshitz field theories with anisotropic scaling, including holographic derivations.

Findings

Distinct power law dependencies of boundary currents on distance from the boundary.

Holographic duality confirms the field theory results for current behavior.

Temporal and spatial components of the current show different boundary condition dependencies.

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.