What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries

Abstract

We survey recent developments in a novel kind of generalized global symmetry, the non-invertible symmetry, in diverse spacetime dimensions. We start with several different but related constructions of the non-invertible Kramers-Wannier duality symmetry in the Ising model, and conclude with a new interpretation for the neutral pion decay and other applications. These notes are based on lectures given at the TASI 2023 summer school "Aspects of Symmetry."

Comments: 95 pages. Many figures, tables, Lagrangians, and Hamiltonians, with a hint of category theory. v2: minor changes