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

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(Nc) gauge theories with fermions transforming according to two different representations. We first study a theory with Nf fermions in the fundamental representation and Nf′ fermions in the adjoint or symmetric or antisymmetric rank-2 tensor representation, in the limit Nc→∞, Nf→∞ with Nf/Nc fixed and finite. We then study the Nc→∞ limit of a theory with fermions in the adjoint and rank-2 symmetric or antisymmetric tensor representations.