Instability in scalar channel of fermion-antifermion scattering amplitude in massless QED_3 and anomalous dimensions of composite operators

TL;DR

This paper investigates the instability in the scalar channel of fermion-antifermion scattering in massless QED_3 for certain flavor numbers, and calculates anomalous dimensions of composite operators, demonstrating infrared logarithm exponentiation.

Contribution

It provides the first analysis of scalar channel instability in massless QED_3 and computes anomalous dimensions to order 1/N, with explicit demonstration of infrared logarithm exponentiation.

Findings

Instability occurs for flavor numbers less than 128/3π^2.

Anomalous dimensions of composite operators are calculated to O(1/N).

Infrared logarithms are shown to exponentiate explicitly.

Abstract

Instability in the scalar channel of the fermion-antifermion scattering amplitude in massless QED_3 for number of flavours less than the critical value 128/3\pi^2 is demonstrated. The anomalous dimensions of gauge-invariant composite operators are determined to O(1/N). Exponentiation of the O(1/N) infrared logarithm is explicitly demonstrated by evaluating the contribution of the ladder diagrams.