Find non-super-bordism methods to access refined field-theoretic invariants

Identify an alternative mathematical framework, outside super bordism categories, that can access the refined equivariant Chern character information of 1|1-dimensional Euclidean field theories over smooth stacks X.

Background

The authors explain that super-geometry in bordism categories is essential to obtain refined invariants like equivariant Chern characters from 1|1-dimensional field theories over stacks.

They explicitly note a lack of alternative approaches capable of extracting this refined information without the super-bordism framework, highlighting an opportunity for methodological development.