Non-local Non-Abelian Gauge Theory: Conformal Invariance and $\beta$-function

TL;DR

This paper extends non-local gauge theories from Abelian to non-Abelian cases, showing the gauge coupling's behavior leads to an asymptotically conformal theory at high energies, with implications for understanding gauge invariance and renormalization.

Contribution

It introduces a non-local non-Abelian SU(N) gauge theory framework and calculates its RGEs, revealing conformal behavior at high energies, extending previous Abelian models.

Findings

Reproduces local $eta$-function in the limit M → ∞

Gauge coupling stops running beyond scale M

Approaches an asymptotically conformal theory

Abstract

This paper focuses on extending our previous discussion of an Abelian U(1) gauge theory involving infinite derivatives to a non-Abelian SU(N) case. The renormalization group equation (RGEs) of the SU(N) gauge coupling is calculated and shown to reproduce the local theory $\beta$-function in the limit of the non-local scale M $\rightarrow \infty$. Interestingly, the gauge coupling stops its running beyond the scale $M$, approaching an asymptotically conformal theory.