Regulator-independent computation of the SGYM four-point function

Compute the one-loop four-point function of three-dimensional supersymmetric Galilean Yang–Mills in a regularization scheme other than the gauge-invariance-violating temporal point-splitting prescription, in order to determine whether the logarithmic divergence is regulator-dependent.

Background

The one-loop four-point function of the charged gauge-sector fields contains a logarithmic divergence that cannot be absorbed into the existing quartic gauge-field terms. The calculation uses temporal point-splitting for Schrödinger propagators, a prescription that violates gauge invariance, so the physical status and scheme dependence of the divergence remain unresolved.

A different regularization scheme could establish whether the divergence is intrinsic to the theory or an artifact of the chosen propagator prescription.

References

As we have used the gauge-invariance violating temporal point-splitting regularization scheme eq: propagator time splitting for the Schr"odinger propagators, one may wonder to what extent the result we have obtained here is regulator-dependent. It would therefore be illuminating to compute the four-point function in a different scheme, which we leave to future work.

— Quantum Effects in Supersymmetric Galilean Yang-Mills  (2608.18843 - Lambert et al., 19 Aug 2026) in Section 3, subsection “Quantizing the Gauge Sector”