Eight dimensional QCD at one loop

Understand

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.