Deformation classes of invertible field theories and the Freed–Hopkins conjecture

Abstract: In their seminal work, Freed and Hopkins studied the moduli space of topological, reflection positive, invertible, Euclidean field theories, providing a complete classification in terms of certain objects arising in stable homotopy theory. In this work, it was also conjectured that a similar classification holds in the case of nontopological field theories, and this conjecture is already being used in a variety of applications to condensed matter physics. In this talk, I will discuss a recent result which provides an affirmative answer to this conjecture. I will begin by reviewing motivation and background on reflection positive theories. Then I will state the conjecture and sketch of the proof.

mathematical physicsalgebraic topologycategory theory

Audience: researchers in the topic

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Topology and Geometry Seminar (Texas, Kansas)