Conformal anomaly transport induced by dark photon

TL;DR

This paper investigates how inhomogeneous gravitational fields affect transport phenomena in massless Dirac fermions within a dark photon model, revealing corrections to conductivities linked to beta functions.

Contribution

It introduces a simplified model for dark sector influence on transport effects, deriving explicit corrections to conductivities without complex quantum field theory in curved spacetime.

Findings

Currents from visible and dark sectors are proportional to beta functions.

Predicted corrections to scale conductivities: linear in dark sector coupling, quadratic in visible sector.

Model simplifies calculations by assuming slight conformal differences from Minkowski spacetime.

Abstract

We have considered the problem of the influence of inhomogeneity of gravitational field on transport effects predicted by the field theory describing massless Dirac fermions in the Maxwell and dark matter background. As a model of dark sector one takes into account dark photon model, where the hidden sector is described by the auxiliary U(1)-gauge field coupled to the visible sector. Elaborating the model we restrict our considerations to the case when Weyl type conformal transformation slightly differs from the Minkowski spacetime. This assumption simplifies the calculations and enables us not to use complicated methods of the quantum field theory in the curved background. The resulting currents stemming both from visible and dark sectors are proportional to the adequate beta functions appearing in the elaborated systems. For charge-less dark sector we predict corrections to the scale conductivities in both sectors: linear in {\alpha} in the dark sector and quadratic in the visible one.