Regarding confinement and dynamical chiral symmetry breaking in QED3

TL;DR

This paper investigates the conditions under which QED3 exhibits a critical number of flavors for dynamical chiral symmetry breaking, emphasizing the importance of homogeneous functions in the infrared and introducing an order parameter for confinement.

Contribution

It establishes the necessary conditions involving homogeneous functions for N_f^c in QED3 and links chiral symmetry restoration with deconfinement through fermion propagator properties.

Findings

Existence of a critical flavor number N_f^c depends on vertex form.

Homogeneity of functions at infrared momenta is crucial.

Chiral symmetry restoration coincides with deconfinement.

Abstract

We establish that QED3 can possess a critical number of flavours, N_f^c, associated with dynamical chiral symmetry breaking if, and only if, the fermion wave function renormalisation and photon vacuum polarisation are homogeneous functions at infrared momenta when the fermion mass function vanishes. The Ward identity entails that the fermion-photon vertex possesses the same property and ensures a simple relationship between the homogeneity degrees of each of these functions. Simple models for the photon vacuum polarisation and fermion-photon vertex are used to illustrate these observations. The existence and value of N_f^c are contingent upon the precise form of the vertex but any discussion of gauge dependence is moot. We introduce an order parameter for confinement. Chiral symmetry restoration and deconfinement are coincident owing to an abrupt change in the analytic properties of the fermion propagator when a nonzero scalar self-energy becomes insupportable.