Non Perturbative Solutions and Scaling Properties of Vector, Axial--Vector Electrodynamics in $1+1$ Dimensions

TL;DR

This paper investigates a non-perturbative vector, axial-vector field theory in 1+1 dimensions, revealing two parameter regimes with distinct physical properties, including fermion confinement and scaling behaviors.

Contribution

It introduces a non-perturbative analysis of a vector, axial-vector model with a parameter interpolating between different Schwinger models, identifying two solution windows with unique features.

Findings

Two parameter windows with acceptable solutions identified.

Fermion confinement occurs in the second window.

Different scaling exponents for fermionic correlators at short and long distances.

Abstract

We study by non perturbative techniques a vector, axial--vector theory characterized by a parameter which interpolates between pure vector and chiral Schwinger models. Main results are two windows in the space of parameters which exhibit acceptable solutions. In the first window we find a free massive and a free massless bosonic excitations and interacting left--right fermions endowed with asymptotic \hbox{states}, which feel however a long range interaction. In the second window the massless bosonic excitation is a negative norm state which can be consistently expunged from the ``physical" Hilbert space; fermions are confined. An intriguing feature of our model occurs in the first window where we find that fermionic correlators scale at both short and long distances, but with different critical exponents. The infrared limit in the fermionic sector is nothing but a dynamically generated massless Thirring model.