Classification of invertible field theories by Anderson dual bordism groups

Establish that invertible field theories are classified by the Anderson dual of the appropriate bordism groups.

Background

The paper formulates worldsheet anomalies as invertible field theories in one dimension higher and employs the Anderson dual of bordism theory to classify them. The authors state that the classification of invertible field theories by the Anderson dual of bordism groups is conjectural, while noting that the explicit model constructed by Yamashita and Yonekura provides supporting evidence.

Resolving this conjecture would provide a general mathematical foundation for the anomaly-classification framework used for Type II and Type I worldsheet theories, including the identification of global anomalies and their differential refinements.

References

In addition, it is conjectured that such invertible field theories are classified by the Anderson dual of bordism groups. Yamashita and Yonekura constructed an explicit model of the Anderson dual group and its differential extension, which supports this conjecture.

— Anomalies and discrete torsion in Type II and Type I worldsheet theories  (2608.30774 - Kawahira et al., 31 Aug 2026) in Section 2.1, “Anomalies as invertible QFT”