Free-to-Interacting Maps and the Bott Spiral
Organizers
Speaker
Cameron Krulewski
Time
Tuesday, December 10, 2024 9:40 AM - 11:15 AM
Venue
A3-2-301
Online
Zoom 468 248 1222
(BIMSA)
Abstract
Free (i.e., noninteracting) and interacting classifications for certain fermionic symmetry-protected topological phases (SPTs) can be compared using homotopical "free-to-interacting maps." We construct such maps to study the phenomenon of the "Bott spiral" of Queiroz-Khalaf-Stern, who observed that the tenfold way classification of free theories breaks down to a large 2-torsion classification in the presence of interactions. Using K-theory and (Anderson-dual) twisted spin bordism, we compute the same interacting classification and interpret the "spiral" as a failure of Morita invariance. Time permitting, I will also discuss how to model dimensional reduction and symmetry breaking for the Bott spiral in terms of homotopy theory.
This talk is based on upcoming work joint with Arun Debray, Natalia Pacheco-Tallaj, and Luuk Stehouwer.
This talk is based on upcoming work joint with Arun Debray, Natalia Pacheco-Tallaj, and Luuk Stehouwer.