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

TL;DR

This paper surveys recent advances in non-invertible symmetries, a new type of generalized global symmetry, highlighting their constructions, interpretations, and applications across various spacetime dimensions.

Contribution

It provides a comprehensive overview of non-invertible symmetries, including new interpretations and applications, based on lectures from TASI 2023.

Findings

Construction of non-invertible Kramers-Wannier duality in the Ising model

New interpretation for neutral pion decay involving non-invertible symmetries

Applications of non-invertible symmetries in diverse spacetime dimensions

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."