A Goldstone theorem for continuous non-invertible symmetries

TL;DR

This paper introduces a new type of non-invertible symmetry charge defect labeled by a continuous U(1), and proves a Goldstone theorem analogue for these symmetries, with potential implications for string theory.

Contribution

It presents a novel construction of non-invertible charge defects with continuous labels and establishes a Goldstone theorem analogue for such symmetries.

Findings

Defined a new non-invertible charge defect with local current operators

Proved an analogue of Goldstone's theorem for continuous non-invertible symmetries

Discussed potential applications to string theory

Abstract

We study systems with an Adler-Bell-Jackiw anomaly in terms of non-invertible symmetry. We present a new kind of non-invertible charge defect where a key role is played by a local current operator localized on the defect. The charge defects are now labeled by elements of a continuous $U(1)$. We use this construction to prove an analogue of Goldstone's theorem for such non-invertible symmetries. We comment on possible applications to string theory.