Eight dimensional QCD at one loop

TL;DR

This paper constructs and analyzes an eight-dimensional non-abelian gauge theory, computing its renormalization group functions and demonstrating its universality class relation to QCD and the non-abelian Thirring model.

Contribution

It introduces an eight-dimensional QCD-like Lagrangian, computes one-loop renormalization group functions, and explores its universality class and operator mixing.

Findings

Eight-dimensional Lagrangian shares universality with QCD and Thirring model.

Computed one-loop renormalization group functions for specific N_c values.

Analyzed mixing matrix of dimension 8 operators in pure Yang-Mills theory.

Abstract

The Lagrangian for a non-abelian gauge theory with an $SU(N_{\! c})$ symmetry and a linear covariant gauge fixing is constructed in eight dimensions. The renormalization group functions are computed at one loop with the special cases of $N_{\! c}$ $=$ $2$ and $3$ treated separately. By computing the critical exponents derived from these in the large $N_{\! f}$ expansion at the Wilson-Fisher fixed point it is shown that the Lagrangian is in the same universality class as the two dimensional non-abelian Thirring model and Quantum Chromodynamics (QCD). As the eight dimensional Lagrangian contains new quartic gluon operators not present in four dimensional QCD, we compute in parallel the mixing matrix of four dimensional dimension $8$ operators in pure Yang-Mills theory.