Mean string field theory: Landau-Ginzburg theory for 1-form symmetries

Iqbal, Nabil; McGreevy, John

Abstract

By analogy with the Landau-Ginzburg theory of ordinary zero-form symmetries, we introduce and develop a Landau-Ginzburg theory of one-form global symmetries, which we call mean string field theory. The basic dynamical variable is a string field – defined on the space of closed loops – that can be used to describe the creation, annihilation, and condensation of effective strings. Like its zero-form cousin, the mean string field theory provides a useful picture of the phase diagram of broken and unbroken phases. We provide a transparent derivation of the area law for charged line operators in the unbroken phase and describe the dynamics of gapless Goldstone modes in the broken phase. The framework also provides a theory of topological defects of the broken phase and a description of the phase transition that should be valid above an upper critical dimension, which we discuss. We also discuss general consequences of emergent one-form symmetries at zero and finite temperature.

Citation

Iqbal, N., & McGreevy, J. (2022). Mean string field theory: Landau-Ginzburg theory for 1-form symmetries. SciPost Physics, 13(5), Article 114. https://doi.org/10.21468/scipostphys.13.5.114

• Journal Article Type: Article
• Acceptance Date: Sep 28, 2022
• Online Publication Date: Nov 22, 2022
• Publication Date: 2022
• Deposit Date: Nov 23, 2022
• Publicly Available Date: Nov 23, 2022
• Journal: SciPost Physics
• Print ISSN: 2542-4653
• Electronic ISSN: 2542-4653
• Publisher: SciPost
• Peer Reviewed: Peer Reviewed
• Volume: 13
• Issue: 5
• Article Number: 114
• DOI: https://doi.org/10.21468/scipostphys.13.5.114
• Public URL: https://durham-repository.worktribe.com/output/1185553