Five-loop Anomalous Dimensions of Cubic Scalar Theory from Operator Product Expansion

Abstract: Recently, an Operator Product Expansion method has been proposed for renormalization in quantum field theories. This method extracts UV divergences from two-point propagator-type integrals, and it is believed to be applicable to generic QFTs. In the present work, we apply the OPE method to the renormalization of scalar theory with cubic interactions in six-dimensions. We have successfully computed the 5-loop corrections to the anomalous dimensions of the $\phi^Q$ operator, as well as the large $N$ expansion of scaling dimensions at the Wilson-Fisher fixed point to $1/N^5$ order. This computation sets a new loop-order record for the anomalous dimension of the $\phi^Q$ operator in cubic scalar theory, and further demonstrates the efficiency and capacity of the OPE method in renormalization.