A Curious Braided Category over R

Abstract: In quantum mechanics, time reversal symmetry is generally understood in terms of an antiunitary operator. When a fusion category over C has an antiunitary symmetry, the fixed points of such a symmetry form a fusion category over the real numbers. Since fusion categories are meant to describe systems of particles, the resulting real fusion category describes those particles that are time-reversal invariant. In recent joint work with Thibault Décoppet (https://arxiv.org/abs/2412.15019), we discovered a certain braided fusion category over R that represents a higher dimensional analogue of the quaternions. Based on recent conjectures regarding the Witt group of nondegenerate braided fusion categories, we expect that this category generates the kernel of the map Witt(Vec_R)->Witt(Vec_C), which is just Z/2. In this talk, I will describe this curious category: its fusion rules and braiding, how it comes about, and it's significance from the perspective of condensed matter.

Mathematics

Audience: researchers in the topic

European Quantum Algebra Lectures (EQuAL)

Series comments: EQuAL is an online seminar series on quantum algebra and related topics such as topological and conformal field theory, operator algebra, representation theory, quantum topology, etc. sites.google.com/view/equalseminar/home