RTGC Seminar: “Spin-statistics” is a categorification of “Hermitian”

Seminar | February 22 | 2:10-3 p.m. | 891 Evans Hall

 Theo Johnson-Freyd, Northwestern University

 Department of Mathematics

I will describe a “cobordism” language in which to pose requirements on a quantum field theory like being Hermitian (when complex conjugation = orientation reversal) or satisfying Spin-Statistics (when fermions = spinors). This language also a homotopy-theoretic origin for those two requirements: nature distinguished them among all possible similar requirements. Namely, Hermitian field theories arise because $\pi _0(\mathrm O(\infty ))$ has a unique nontrivial torsor over $\mathrm {Spec}(\mathbb R)$. Spin-statistics field theories arise for the same reason, except that one must replace $\pi _0(\mathrm O(\infty ))$ with the fundamental groupoid of $\mathrm O(\infty )$ and one must replace commutative algebras with symmetric monoidal categories.