Non-Invertible Symmetries, Anomalies and Scattering Amplitudes

TL;DR

This paper explores how non-invertible symmetries and anomalies modify crossing symmetry in two-dimensional integrable quantum field theories, leading to new consistent S-matrix formulations that obey fusion category rules.

Contribution

It introduces a framework for understanding how non-invertible symmetries alter crossing symmetry in S-matrices, extending to theories with discrete anomalies.

Findings

Standard bootstrap S-matrices are incompatible with non-invertible symmetries.

Proposes alternative S-matrices obeying modified crossing rules.

Extends the framework to theories with discrete anomalies.

Abstract

We show that crossing symmetry of S-matrices is modified in certain theories with non-invertible symmetries or anomalies. Focusing on integrable flows to gapped phases in two dimensions, we find that S-matrices derived previously from the bootstrap approach are incompatible with non-invertible symmetries along the flow. We present consistent alternatives, which however violate standard crossing symmetry and obey modified rules dictated by fusion categories. We extend these rules to theories with discrete anomalies.