Work out the supersymmetric extension of the degree twist in the bordism framework

Develop a complete supersymmetric extension of the chiral degree twist within the Stolz–Teichner cobordism framework—providing explicit definitions and verification in both Ramond and Neveu–Schwarz sectors—and establish its functorial properties.

Background

The degree twist in dimension 2|1 is chiral and expected to admit a canonical supersymmetric extension, generalizing the chiral-to-supersymmetric passage familiar in 2D QFT.

Despite this expectation, the authors state that the details of such an extension in the cobordism framework have not been worked out, leaving a concrete technical gap.