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

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Cited by in corpus (8)

• The effective action for gauge bosons
• Two-Loop anomalous dimensions of QCD operators up to dimension-sixteen and Higgs EFT amplitudes
• Operator mixing in massless QCD-like theories and Poincare'-Dulac theorem
• Gluonic evanescent operators: classification and one-loop renormalization
• Gluonic evanescent operators: two-loop anomalous dimensions
• Algebraic Interplay between Renormalization and Monodromy
• Operator mixing, UV asymptotics of nonplanar/planar $2$-point correlators, and nonperturbative large-$N$ expansion of QCD-like theories
• Some aspects of CP violation and gauge interactions in the standard model and beyond