R-symmetry in the Q-exact (2,2) 2d lattice Wess-Zumino model

TL;DR

This study investigates the R-symmetry in the lattice formulation of the (2,2) 2d Wess-Zumino model, demonstrating its approximate realization and nonperturbative recovery of continuum properties through Monte Carlo simulations.

Contribution

It provides nonperturbative evidence that R-symmetry is effectively realized in the lattice model and that the continuum nonrenormalization theorem is recovered.

Findings

R-symmetry is a symmetry of the effective potential

No additive mass renormalization observed in the continuum limit

Fourier acceleration improves Monte Carlo simulation efficiency

Abstract

In this article we explore the R-symmetry of the (2,2) 2d Wess-Zumino model. We study whether or not this symmetry is approximately realized in the Q-exact lattice version of this theory. Our study is nonperturbative: it relies on Monte Carlo simulations with dynamical fermions. Irrelevant operators in the lattice action explicitly break the R-symmetry. In spite of this, it is found to be a symmetry of the effective potential. We find nonperturbative evidence that the nonrenormalization theorem of the continuum theory is recovered in the continuum limit; e.g., there is no additive mass renormalization. In our simulations we find that Fourier acceleration of the hybrid Monte Carlo algorithm allows us to avoid difficulties with critical slowing-down.