Particle-Soliton Degeneracies from Spontaneously Broken Non-Invertible Symmetry

TL;DR

This paper investigates how non-invertible topological symmetries in (1+1)d quantum field theories lead to particle degeneracies in broken phases, providing a general method to determine allowed multiplets without requiring integrability.

Contribution

It introduces a procedure to identify particle multiplet degeneracies caused by non-invertible symmetries in massive quantum field theories, applicable beyond integrable models.

Findings

Degeneracies are dictated by non-invertible symmetries in broken phases.

The method applies to known models like the Tricritical Ising model.

Degeneracies relate soliton and particle spectra through fusion categories.

Abstract

We study non-invertible topological symmetry operators in massive quantum field theories in (1+1) dimensions. In phases where this symmetry is spontaneously broken we show that the particle spectrum often has degeneracies dictated by the non-invertible symmetry and we deduce a procedure to determine the allowed multiplets. These degeneracies are robust predictions and do not require integrability or other special features of renormalization group flows. We exhibit these conclusions in examples where the spectrum is known, recovering soliton and particle degeneracies. For instance, the Tricritical Ising model deformed by the subleading Z2 odd operator flows to a gapped phase with two degenerate vacua. This flow enjoys a Fibonacci fusion category symmetry which implies a threefold degeneracy of its particle states, relating the mass of solitons interpolating between vacua and particles supported in a single vacuum.