Four loop renormalization in six dimensions using forcer

Abstract

We employ the algorithm to renormalize a variety of six dimensional field theories to four loops. In order to achieve this we construct the master integrals in six dimensions from their four dimensional counterparts by using the Tarasov method. The ε expansion of the six dimensional masters are determined up to weight 9 where d=6−2ε. By applying the routine the four loop MS¯ renormalization of ϕ3 theory is reproduced before gauge theories are considered. The renormalization of these theories is also determined in the MOM˜ scheme. For instance the absence of ζ4 and ζ6 is confirmed to five loops in the MOM˜ renormalization of ϕ3 theory. We also evaluate the three loop β-function of the gauge coupling in six dimensional QCD. Published by the American Physical Society 2024