Asymptotic safety in the Litim-Sannino model at four loops

We consider a four-dimensional $SU(N_c)$ gauge theory coupled to $N_f$ species of color fermions and $N_f^2$ colorless scalars. The quantum field theory possesses a weakly interacting ultraviolet fixed point that we determine from beta functions computed up to four-loop order in the gauge coupling, and up to three-loop order in the Yukawa and quartic scalar couplings. The fixed point has one relevant direction giving rise to asymptotic safety. We compute fixed point values of dimensionless couplings together with the corresponding scaling exponents up to the first three nontrivial orders in Veneziano parameter $\epsilon$, both for infinite and finite number of colors $N_c$. We also consider anomalous dimensions for fields, scalar mass squared, and a class of dimension-three operators. Contrary to previous studies, we take into account possible mixing of the latter and compute eigenvalues of the corresponding matrix. Further, we investigate the size of the conformal window in the Veneziano limit and its dependence on $N_c$.