A Goldstone theorem for continuous non-invertible symmetries

Iñaki García Etxebarria; Nabil Iqbal

A Goldstone theorem for continuous non-invertible symmetries

High Energy Physics - Theory 2022-11-21 v2 Strongly Correlated Electrons

Authors: Iñaki García Etxebarria , Nabil Iqbal

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.

Keywords

non-invertible symmetry goldstone theorem adler-bell-jackiw anomaly u(1) charge defect string theory

Cite

@article{arxiv.2211.09570,
  title  = {A Goldstone theorem for continuous non-invertible symmetries},
  author = {Iñaki García Etxebarria and Nabil Iqbal},
  journal= {arXiv preprint arXiv:2211.09570},
  year   = {2022}
}

Comments

16 pages, 1 very simple figure; v2: Fixed a mistake in section 2.4, main conclusions unchanged

A Goldstone theorem for continuous non-invertible symmetries

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