Non-Invertible Symmetries, Anomalies and Scattering Amplitudes

TL;DR

The work addresses how crossing symmetry of two-dimensional S-matrices is altered in theories with non-invertible categorical symmetries and discrete anomalies, focusing on integrable flows to gapped phases. By deriving Ward identities and analyzing consistency with symmetry data, the authors show that standard crossing cannot hold alongside unitarity, Yang-Baxter, and non-invertible symmetries. They construct S-matrices that satisfy unitarity and Yang-Baxter while obeying modified crossing rules dictated by fusion-category data, and extend the framework to the Z2 anomaly in perturbed SU(2)1 WZW models and phi21 deformations of tricritical Ising. The results offer a categorical mechanism for IR TQFT effects on scattering and invite further exploration of modified crossing in higher dimensions and with broader fusion categories.

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.

Figures (1)

• Figure 1: Kinks (solid lines) and anti-kinks (dashed lines) connecting the minima of the potential. Both come with two-fold degeneracy (blue and yellow) due to the Kramers degeneracy.