Homotopical Methods for Free and Interacting Fermionic SPTs

We develop and compute homotopical “free-to-interacting maps” to compare classifications of fermionic symmetry-protected topological phases (SPTs), determining when such phases are stable under interactions or, alternatively, interaction-enabled. Generalizing work of Freed-Hopkins, we construct maps from K-theory to Anderson-dual spin bordism in two new situations: for weak phases, which are SPTs protected by discrete translation symmetry, and for the “Bott spiral” studied by Queiroz-Khalaf-Stern, who observed that the tenfold way classification of free theories breaks down to a large 2-torsion interacting classification. Along the way, we employ T-duality, generalizations of the spin orientation of KO-theory, and the Adams spectral sequence.

This talk is based on joint work with Omar Antolín Camarena, Arun Debray, Natalia Pacheco-Tallaj, Daniel Sheinbaum, and Luuk Stehouwer.

In person and online:

Zoom link: https://harvard.zoom.us/j/97784644596
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