MathDBFusion categories admit spin field theory structures
Fusion categories admit spin field theory structures
Let be a fusion category over an algebraically closed field of characteristic zero. A homotopy fixed point structure on is the additional structure corresponding, under the cobordism hypothesis, to a spin 3-dimensional local field theory. Spin descent conjecture. Every fusion category is a homotopy fixed point, and therefore provides a spin local field theory. This is the strongest of the three stated anomaly-vanishing conjectures in the supplied passage, following the oriented and combed descent conjectures; the supplied text gives no resolution status.
Sources & referencesView supporting material
Primary source
Christopher L. Douglas, Christopher Schommer-Pries and Noah Snyder, “Dualizable tensor categories”, arXiv:1312.7188 (2018).
Progress summary
A 2026 preprint claims to prove that every fusion category gives a spin field theory, but independent confirmation has not been recorded.
The spin descent conjecture asks whether every fusion category carries the structure needed to define a spin field theory. The new paper identifies this as a conjecture of DSPS and claims to settle the corresponding invariance statement.
2026 preprint claim
The paper proves that the action on fusion super-categories has trivial obstruction and unique invariance data, then states that this settles the DSPS conjecture. It also says the corresponding assertion for fusion categories was conjectured there. The retrieved material does not explicitly restate the exact claim for every ordinary fusion category, so this is reported as an unverified resolution rather than a settled theorem.
Current status (as of August 2026): A 2026 preprint claims to resolve the conjecture, but the exact ordinary-fusion-category implication and its proof have not been independently verified in the retrieved sources.
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