Abstract
In previous work we have presented scheme-independent calculations of physical properties of operators at a conformally invariant infrared fixed point in an asymptotically free gauge theory with gauge group $G$ and $N_f$ fermions in a representation $R$ of $G$. Here we generalize this analysis to the case of fermions in multiple representations, focusing on the case of two different representations. Our results include the calculation of the anomalous dimensions of gauge-invariant fermion bilinear operators, and the derivative of the beta function, evaluated at the infrared fixed point. We illustrate our results in an SU($N_c$) gauge theory with $N_F$ fermions in the fundamental representation and $N_{Adj}$ fermions in the adjoint representation.
Highlights
In this paper we shall consider a vectorial, asymptotically free gauge theory with gauge group G with massless fermions transforming according to multiple different representations of G, which has an exact infrared (IR) fixed point (IRFP) of the renormalization group [1]
One motivation for such theories is a possible direction for ultraviolet completions of the Standard Model that might help to explain the origin of the generational hierarchy of quark and lepton masses (e.g., [2,3] and references therein), since this hierarchy could be associated with the different Euclidean energy/momentum scales at which fermion condensates form for fermions in different representations of a strongly coupled gauge interaction involving beyond-Standard-Model (BSM) physics
For theories with Nf fermions in a single representation of the gauge group G, we have calculated scheme-independent series expansions for the anomalous dimensions of gauge-invariant fermion bilinears and the derivative dβ=dα, both evaluated at the IRFP, to the respective orders OðΔ4fÞ and OðΔ5fÞ [11,12,13,14,15,16,17,18,19]
Summary
In this paper we shall consider a vectorial, asymptotically free gauge theory (in four spacetime dimensions, at zero temperature) with gauge group G with massless fermions transforming according to multiple different representations of G, which has an exact infrared (IR) fixed point (IRFP) of the renormalization group [1]. For theories with Nf fermions in a single representation of the gauge group G, we have calculated scheme-independent series expansions for the anomalous dimensions of gauge-invariant fermion bilinears and the derivative dβ=dα, both evaluated at the IRFP, to the respective orders OðΔ4fÞ and OðΔ5fÞ [11,12,13,14,15,16,17,18,19]. These are the highest orders to which these quantities have been calculated. VII, and some relevant group-theoretic results are reviewed in Appendix
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