Five-loop anomalous dimensions of ${\varphi }^Q$ operators in a scalar theory with $O(N)$ symmetry

Abstract

We compute the complete $Q$-dependence of anomalous dimensions of traceless symmetric tensor operator ${\varphi }^Q$ in $O(N)$ scalar theory to five-loop. The renormalization factors are extracted from ${\varphi }^Q\to Q\varphi$ form factors, and the integrand of form factors are constructed with the help of unitarity cut method. The anomalous dimensions match the known results in \cite{Badel:2019oxl, Antipin:2020abu}, where the leading and subleading terms in the large $Q$ limit were obtained using a semiclassical method.

arXiv comment17 pages, 9 figures