Ward Identities for Transport in 2+1 Dimensions

TL;DR

This paper derives relations between transport coefficients in 2+1 dimensional systems using Ward identities, applicable to various symmetries and including effects of magnetic fields, with validation from effective theories and holography.

Contribution

It introduces a unified approach using Ward identities to relate transport coefficients across different 2+1D systems with various symmetries and external conditions.

Findings

Relations match effective theory results for Hall fluids

Consistent with holographic calculations in black hole backgrounds

Applicable to systems with broken translation symmetry and magnetic fields

Abstract

We use the Ward identities corresponding to general linear transformations, and derive relations between transport coefficients of $(2+1)$-dimensional systems. Our analysis includes relativistic and Galilean invariant systems, as well as systems without boost invariance such as Lifshitz theories. We consider translation invariant, as well as broken translation invariant cases, and include an external magnetic field. Our results agree with effective theory relations of incompressible Hall fluid, and with holographic calculations in a magnetically charged black hole background.