Ultraviolet Fixed Points in Gauge and SUSY Field Theories in Extra Dimensions

TL;DR

This paper demonstrates the existence of nonperturbative ultraviolet fixed points in gauge and supersymmetric field theories in higher dimensions, leading to conformal invariance and exact anomalous dimensions.

Contribution

It reveals the presence of ultraviolet fixed points in higher-dimensional gauge and SUSY theories, providing exact anomalous dimensions and establishing conformal invariance.

Findings

Ultraviolet fixed points exist in $D>4$ gauge theories.

Fixed points are nonperturbative and conformally invariant.

Exact anomalous dimensions are known at the fixed points.

Abstract

We consider gauge field theories in $D>4$ following the Wilson RG approach and show that they possess the ultraviolet fixed points where the gauge coupling is dimensionless in any space-time dimension. At the fixed point the anomalous dimensions of the field and vertex operators are known exactly. These fixed points are nonperturbative and correspond to conformal invariant theories. The same phenomenon also happens in supersymmetric theories with the Yukawa type interactions.