Massless Three Dimensional Quantum Electrodynamics and Thirring Model Constrained by Large Flavor Number

TL;DR

This paper compares the infrared and ultraviolet degrees of freedom in three-dimensional massless QED and Thirring models at large flavor numbers, revealing contrasting behaviors linked to asymptotic freedom.

Contribution

It provides an explicit proof of the infrared degrees of freedom constraints in 3D massless QED and highlights the reversal in Thirring model due to its coupling behavior.

Findings

Infrared degrees of freedom are never larger than ultraviolet in 3D massless QED.

The Thirring model exhibits a reversal of this behavior due to positive running coupling derivative.

Asymptotic freedom plays a crucial role in the infrared-ultraviolet relationship.

Abstract

We explicitly prove that in three dimensional massless quantum electrodynamics at finite temperature, zero density and large number of flavors the number of infrared degrees of freedom is never larger than the corresponding number of ultraviolet. Such a result, strongly dependent on the asymptotic freedom of the theory, is reversed in three dimensional Thirring model due to the positive derivative of its running coupling constant.