Eight dimensional QCD at one loop

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.

31 latex pages, anc directory now added which contains txt file of all renormalization group functions

References in corpus (6)

• The five-loop beta function of Yang-Mills theory with fermions
• Critical $O(N)$ Models in $6-\epsilon$ Dimensions
• The five-loop Beta function for a general gauge group and anomalous dimensions beyond Feynman gauge
• Five-loop quark mass and field anomalous dimensions for a general gauge group
• Five-loop renormalisation of QCD in covariant gauges
• Three Loop Analysis of the Critical $O(N)$ Models in $6-\epsilon$ Dimensions