Critical Wess-Zumino models with four supercharges from the functional renormalization group

TL;DR

This paper studies the fixed points and critical exponents of a supersymmetric Wess-Zumino model in three dimensions using the functional renormalization group, revealing detailed properties of the superpotential and K"ahler metric.

Contribution

It provides a detailed analysis of non-trivial fixed points and critical exponents in a supersymmetric model using the functional renormalization group, including the explicit form of the K"ahler metric.

Findings

Fixed points and critical exponents are computed.

The K"ahler metric at the fixed point is explicitly determined.

The quantum dimension of the chiral superfield is obtained.

Abstract

We analyze the $\mathcal{N}=1$ supersymmetric Wess-Zumino model dimensionally reduced to the $\mathcal{N}=2$ supersymmetric model in three Euclidean dimensions. As in the original model in four dimensions and the $\mathcal{N}=(2,2)$ model in two dimensions the superpotential is not renormalized. This property puts severe constraints on the non-trivial fixed-point solutions, which are studied in detail. We admit a field-dependent wave function renormalization that in a geometric language relates to a K\"ahler metric. The K\"ahler metric is not protected by supersymmetry and we calculate its explicit form at the fixed point. In addition we determine the exact quantum dimension of the chiral superfield and several critical exponents of interest, including the correction-to-scaling exponent $\omega$, within the functional renormalization group approach. We compare the results obtained at different levels of truncation, exploring also a momentum-dependent wave function renormalization. Finally we briefly describe a tower of multicritical models in continuous dimensions.