Photons and Fermions in Spacetime with a Compactified Spatial Dimension

TL;DR

This paper explores how compactified spatial dimensions affect photon and fermion behavior in quantum electrodynamics and gauged-NJL theories, revealing anisotropic photon propagation, superluminal modes, and confinement effects at small radii.

Contribution

It demonstrates the equivalence of twisted and untwisted fermion vacuum effects and analyzes photon mass, superluminal modes, and chiral symmetry breaking dependence on compactification radius.

Findings

Photon modes become massive and anisotropic with decreasing radius.

Photon velocity can be superluminal and increases logarithmically with radius.

Chiral symmetry breaking requires larger coupling at smaller compactification radii.

Abstract

The effects of a nonsimply connected spacetime with the topology of $S^{1}\times R^{3}$ in the vacua of QED and gauged-NJL theories are investigated. It is shown that the polarization effects of twisted and untwisted fermions in QED are equivalent, once the corresponding stable vacuum solution of each fermion class is taken into account. The photon propagation in QED is found to be anisotropic and characterized by several massive photon modes and a superluminal transverse mode. At small compactification radius the masses of the massive modes increase as the inverse of the radius, while the massless photon mode has a superluminal velocity that increases logarithmically with that distance. At low energies the photon masses lead to an effective confinement of the gauge fields into a $(2+1)-$dimensional manifold transverse to the compactified direction. In the gauged-NJL model, it is shown that for both twisted and untwisted fermions, the smaller the compactification radius, the larger the critical four-fermion coupling needed to generate a fermion-antifermion chiral symmetry breaking condensate.