Constraints on an Asymptotic Safety Scenario for the Wess-Zumino Model

TL;DR

This paper proves that an asymptotic safety scenario for the Wess-Zumino model is impossible unless specific conditions involving a non-trivial fixed point are met, based on nonrenormalization and Pohlmeyer's theorems.

Contribution

It establishes necessary conditions for asymptotic safety in the Wess-Zumino model using theoretical theorems, ruling out scenarios lacking these conditions.

Findings

No asymptotic safety without a non-trivial fixed point with negative anomalous dimension.

Relevant direction must belong to the Kaehler potential.

Constraints derived from nonrenormalization and Pohlmeyer's theorems.

Abstract

Using the nonrenormalization theorem and Pohlmeyer's theorem, it is proven that there cannot be an asymptotic safety scenario for the Wess-Zumino model unless there exists a non-trivial fixed point with (i) a negative anomalous dimension (ii) a relevant direction belonging to the Kaehler potential.