S-Matrix Bootstrap and Non-Invertible Symmetries

TL;DR

This paper develops a bootstrap approach for S-matrices in (1+1)D theories with non-invertible symmetries, revealing how modified crossing symmetry constrains possible theories and identifying integrable models at the boundaries.

Contribution

It introduces a novel bootstrap framework incorporating non-invertible symmetries and extends crossing rules using fusion categories and SymTFT, advancing the understanding of such theories.

Findings

Identified constraints on S-matrices with non-invertible symmetries.

Located integrable theories at the boundary of allowed S-matrix space.

Extended crossing symmetry to non-regular vacuum representations.

Abstract

We initiate the S-matrix bootstrap analysis of theories with non-invertible symmetries in (1+1) dimensions. Our previous work showed that crossing symmetry of S-matrices in such theories is modified, with modification characterized by the fusion category data. By imposing unitarity, symmetry and the modified crossing, we constrain the space of consistent S-matrices, identifying integrable theories with non-invertible symmetries at the cusps of allowed regions. We also extend the modified crossing rules to cases where vacua transform in non-regular representations of fusion category, utilizing a connection to a dual category $\mathscr C^{*}_{\mathscr{M}}$ and Symmetry Topological Field Theory (SymTFT). This highlights the utility of SymTFT in the analysis of scattering amplitudes.