Five loop renormalization of the Wess-Zumino model

TL;DR

This paper performs a five-loop renormalization of the Wess-Zumino model in different schemes, computes critical exponents, and compares results with conformal bootstrap estimates, advancing precision in supersymmetric quantum field theories.

Contribution

The work extends renormalization calculations of the Wess-Zumino model to five loops and explores generalizations with O(N) symmetry, providing high-precision critical exponents and beta-function coefficients.

Findings

Five-loop renormalization results in MSbar and MOM schemes.

Critical exponents agree with conformal bootstrap estimates.

Identifies the rational part of the six-loop beta-function.

Abstract

We renormalize the Wess-Zumino model at five loops in both the minimal subtraction (MSbar) and momentum subtraction (MOM) 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 MSbar beta-function.