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

Iqbal, Nabil; McGreevy, John

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


John McGreevy


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.

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
Publisher SciPost
Peer Reviewed Peer Reviewed
Volume 13
Issue 5
Article Number 114
Public URL


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