Anomaly-free perturbative description in one-dimensional worldvolume Wess–Zumino models

Determine whether perturbation theory expanded about free fields yields an anomaly-free description for the auxiliary noise field F(x) = dφ/dx ± ∂W/∂φ(x) in the one-dimensional worldvolume formulation of Wess–Zumino models via the Parisi–Sourlas/Nicolai map, i.e., whether perturbation theory reproduces the stochastic identities (including Wick’s theorem and ⟨F(x)⟩ = ⟨∂W/∂φ(x)⟩) without additional anomaly terms.

Background

In the one-dimensional worldvolume case, identifying the auxiliary field as F(x) = dφ/dx ± ∂W/∂φ(x) allows testing whether the noise-field correlators satisfy Wick’s theorem without anomalies. Monte Carlo simulations reported by the authors indicate no anomalies beyond lattice artifacts.

The explicit unresolved issue is whether standard perturbation theory around free fields can reproduce the same anomaly-free identities for the noise-field correlators, matching the Monte Carlo findings.