The two dimensional N=(2,2) Wess-Zumino Model in the Functional Renormalization Group Approach

TL;DR

This paper applies the functional renormalization group to the 2D N=(2,2) Wess-Zumino model, confirming the nonrenormalization theorem at leading order and exploring quantum corrections at higher orders with a new numerical tool.

Contribution

It introduces a numerical toolbox called FlowPy for solving the FRG equations and extends the analysis beyond leading order, revealing the impact of higher-order operators on the renormalized mass.

Findings

Nonrenormalization theorem holds at leading order.

Quantum corrections match lattice results at weak coupling.

Higher-order operators dominate at intermediate couplings.

Abstract

We study the supersymmetric N=(2,2) Wess-Zumino model in two dimensions with the functional renormalization group. At leading order in the supercovariant derivative expansion we recover the nonrenormalization theorem which states that the superpotential has no running couplings. Beyond leading order the renormalization of the bare mass is caused by a momentum dependent wave function renormalization. To deal with the partial differential equations we have developed a numerical toolbox called FlowPy. For weak couplings the quantum corrections to the bare mass found in lattice simulations is reproduced with high accuracy. But in the regime with intermediate couplings higher-order-operators that are not constrained by the nonrenormalization theorem yield the dominating contribution to the renormalized mass.