Confinement and Renormalization Group Equations in String-inspired Non-local Gauge Theories

TL;DR

This paper explores how non-local gauge theories inspired by string theory can achieve confinement and asymptotic freedom, extending local theory criteria to the non-local context and analyzing their behavior across energy scales.

Contribution

It extends the confinement criterion to non-local gauge theories, demonstrating finite IR contributions and the absence of Landau poles, thus providing insights into UV completion and IR behavior.

Findings

Non-local theories provide finite IR contributions.

Confinement is proven without Landau poles.

IR fixed point moves to infinity in non-local theories.

Abstract

As an extension of the weak perturbation theory obtained in recent analysis on infinite-derivative non-local non-Abelian gauge theories motivated from p-adic string field theory, and postulated as direction of UV-completion in 4-D Quantum Field Theory (QFT), here we investigate the confinement conditions and $\beta-$function in the strong coupling regime. We extend the confinement criterion, previously obtained by Kugo and Ojima for the local theory based on the Becchi-Rouet-Stora-Tyutin (BRST) invariance, to the non-local theory, by using a set of exact solutions of the corresponding local theory. We show that the infinite-derivatives which are active in the UV provides finite contributions also in the infrared (IR) limit and provide a proof of confinement, granted by the absence of the Landau pole. The main difference with the local case is that the IR fixed point is moved to infinity. We also show that in the limit of the energy scale of non-locality $M \rightarrow \infty$ we reproduce the local theory results and see how asymptotic freedom is properly recovered.