Landau-Ginzburg theory for 1-form symmetries

Abstract: To conclude the first block of seminars on higher form symmetry, I will review the first four sections of $\textbf{Mean string field theory: Landau-Ginzburg theory for 1-form symmetries}$ by Nabil Iqbal, John McGreevy.

$\textit{Abstract of the paper:}$

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.

condensed mattergeneral relativity and quantum cosmologyHEP - theorymathematical physicsdifferential geometry

Audience: advanced learners

( paper )

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Europe and Pacific Theoretical Physics

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