Critical exponents from five-loop scalar theory renormalization near six-dimensions

Abstract: We present five-loop results for the renormalization of various models with a cubic interaction (in ${d = 6 - 2 \varepsilon}$ dimensions). For the scalar model and its ${O(n)}$-symmetric extension we provide renormalization constants, anomalous dimensions and critical exponents. We discuss in detail the method of calculation, and provide all counterterms up to five loops. This allows one to consider generalizations of the ${\varphi^3}$ theory to other symmetries.