The Renormalization Group and the Effective Potential in the Wess-Zumino model

TL;DR

This paper analyzes the effective potential in the massless Wess-Zumino model using the renormalization group, showing that the potential becomes flat at extrema, with implications for supersymmetric gauge theories.

Contribution

It demonstrates the cancellation of mu dependence in the effective potential and establishes conditions under which the potential is flat at extrema, advancing understanding of supersymmetric models.

Findings

Mu dependence cancels in the effective potential.

Potential is flat at extrema with non-zero background fields.

Implications for supersymmetric gauge theories are discussed.

Abstract

We consider the effective potential V in the massless Wess-Zumino model. By using the renormalization group equation, we show that the explicit dependence of V on the renormalization mass scale mu cancels. If V has an extremum at some non-vanishing value of the background field, then it follows that V is "flat", independent of the background field. This is consistent with the general requirement that V be complex. The consequences for supersymmetric gauge theories are briefly considered.