Large-$N_c$ and Large-$N_F$ Limits of SU($N_c$) Gauge Theories with Fermions in Different Representations

Abstract

We present calculations of certain limits of scheme-independent series expansions for the anomalous dimensions of gauge-invariant fermion bilinear operators and for the derivative of the beta function at an infrared fixed point in SU($N_c$) gauge theories with fermions transforming according to two different representations. We first study a theory with $N_f$ fermions in the fundamental representation and $N_{f^{\prime }}$ fermions in the adjoint or symmetric or antisymmetric rank-2 tensor representation, in the limit $N_c\to \infty$, $N_f\to \infty$ with $N_f/N_c$ fixed and finite. We then study the $N_c\to \infty$ limit of a theory with fermions in the adjoint and rank-2 symmetric or antisymmetric tensor representations.

18 pages, RevTex

References in corpus (7)

• The five-loop beta function of Yang-Mills theory with fermions
• Higher-Loop Corrections to the Infrared Evolution of a Gauge Theory with Fermions
• Scheme-Independent Series Expansions at an Infrared Zero of the Beta Function in Asymptotically Free Gauge Theories
• Scheme-Independent Calculation of ${\gamma }_{\bar{\psi }\psi ,IR}$ for an SU(3) Gauge Theory
• Infrared Fixed Point Physics in $\mathrm{SO}(N_c)$ and $\mathrm{Sp}(N_c)$ Gauge Theories
• Physics of the Non-Abelian Coulomb Phase: Insights from Padé Approximants
• Scheme-Independent Calculations of Physical Quantities in an $\mathcal{N}=1$ Supersymmetric Gauge Theory

Cited by in corpus (6)

• Lattice simulations of a gauge theory with mixed adjoint-fundamental matter
• Scheme-Independent Series for Anomalous Dimensions of Higher-Spin Operators at an Infrared Fixed Point in a Gauge Theory
• Anomalous Dimensions at an Infrared Fixed Point in an SU($N_c$) Gauge Theory with Fermions in the Fundamental and Antisymmetric Tensor Representations
• Large $N_f$ for multiple representations
• A Comparative Study of Criticality Conditions for Anomalous Dimensions using Exact Results in an $\mathcal{N}=1$ Supersymmetric Gauge Theory
• Baryons, Skyrmions and $\theta$-periodicity anomaly in chiral and vector-like gauge theories