## SciPost Submission Page

# Comments on Abelian Higgs Models and Persistent Order

### by Zohar Komargodski, Adar Sharon, Ryan Thorngren, Xinan Zhou

####
- Published as
SciPost Phys.
**6**,
3
(2019)

### Submission summary

As Contributors: | Adar Sharon · Ryan Thorngren |

Arxiv Link: | https://arxiv.org/abs/1705.04786v4 |

Date accepted: | 2018-12-19 |

Date submitted: | 2018-12-11 |

Submitted by: | Thorngren, Ryan |

Submitted to: | SciPost Physics |

Domain(s): | Theoretical |

Subject area: | High-Energy Physics - Theory |

### Abstract

A natural question about Quantum Field Theory is whether there is a deformation to a trivial gapped phase. If the underlying theory has an anomaly, then symmetric deformations can never lead to a trivial phase. We discuss such discrete anomalies in Abelian Higgs models in 1+1 and 2+1 dimensions. We emphasize the role of charge conjugation symmetry in these anomalies; for example, we obtain nontrivial constraints on the degrees of freedom that live on a domain wall in the VBS phase of the Abelian Higgs model in 2+1 dimensions. In addition, as a byproduct of our analysis, we show that in 1+1 dimensions the Abelian Higgs model is dual to the Ising model. We also study variations of the Abelian Higgs model in 1+1 and 2+1 dimensions where there is no dynamical particle of unit charge. These models have a center symmetry and additional discrete anomalies. In the absence of a dynamical unit charge particle, the Ising transition in the 1+1 dimensional Abelian Higgs model is removed. These models without a unit charge particle exhibit a remarkably persistent order: we prove that the system cannot be disordered by either quantum or thermal fluctuations. Equivalently, when these theories are studied on a circle, no matter how small or large the circle is, the ground state is non-trivial.

###### Current status:

**6**, 3 (2019)