Existence of a supersymmetric QFT for the anomalous superpotential

Establish whether the classical superpotential introduced for anomalous four-dimensional GLSMs, such as the projective-space examples, arises from a sensible supersymmetric quantum field theory.

Background

The paper proposes using a two-dimensional classical superpotential to reproduce quantum elliptic cohomology relations in cases where the corresponding four-dimensional GLSM has gauge anomalies. Because those anomalies obstruct interpreting the construction as a genuine Kaluza–Klein reduction from four dimensions, it is unresolved whether the resulting superpotential has an underlying consistent supersymmetric quantum field theory interpretation.