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

TL;DR

This paper develops a Landau-Ginzburg-like theoretical framework for understanding one-form symmetries using string fields, elucidating phase transitions, topological defects, and Goldstone modes in gauge theories.

Contribution

It introduces mean string field theory as a novel approach to describe one-form symmetries, extending Landau-Ginzburg concepts to higher-form symmetries.

Findings

Derivation of the area law for line operators in the unbroken phase

Description of Goldstone modes in the broken phase

Framework for phase transitions and topological defects

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.