Five loop renormalization of the Wess-Zumino model

We renormalize the Wess-Zumino model at five loops in both the minimal subtraction ((MS) over bar) and momentum subtraction schemes. The calculation is carried out automatically using a routine that performs the D-algebra. Generalizations of the model to include O(N) symmetry as well as the case with real and complex tensor couplings are also considered. We confirm that the emergent SU(3) symmetry of six-dimensional O(N)phi(3) theory is also a property of the tensor O(N) model. With the new loop order precision we compute critical exponents in the epsilon expansion for several of these generalizations as well as the XYZ model in order to compare with conformal bootstrap estimates in three dimensions. For example at five loops our estimate for the correction to scaling exponent is in very good agreement for the Wess-Zumino model which equates to the emergent supersymmetric fixed point of the Gross-Neveu-Yukawa model. We also compute the rational number that is part of the six loop (MS) over bar beta-function.

Automated summary

In this study, the Wess-Zumino model is renormalized at five loops, and some generalizations of the model are considered. Critical exponents are calculated with the new loop order precision and compared with conformal bootstrap estimates.