Jena lectures on generalized global symmetries: principles and applications

2024/07/30 by Nabil Iqbal, Iqbal, Nabil · 6 citations
Mathematics · #Algebraic and Geometric Analysis #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Statistical Mechanics (cond-mat.stat-mech) #Strongly Correlated Electrons (cond-mat.str-el)

paper · pdf · doi:10.48550/arxiv.2407.20815

openalex publication_date 2024/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This is an elementary set of lectures on generalized global symmetries originally given at the Jena TPI School on QFT and Holography, designed to be accessible to the reader with a basic knowledge of quantum field theory. Topics covered include an introduction to higher-form symmetries with selected applications: Abelian and non-Abelian gauge theories in the continuum and on the lattice, statistical mechanical systems, the Adler-Bell-Jackiw anomaly from the point of view of non-invertible symmetry, and magnetohydrodynamics. Mathematical formalism is kept to a minimum and an emphasis is placed on understanding the global symmetry structure present in well-known models.

Cited by

• Spurion Analysis of ℤ_M/ℤ₂ Non-Invertible Selection Rules: Low-Order versus All-Order Zeros
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• Spurion Analysis for Non-Invertible Selection Rules from Near-Group Fusions
• Quantifying non-invertible chiral symmetry breaking
• Generalized Symmetries in Shallow Water
• Higher-form anomalies and state-operator correspondence beyond conformal invariance

Related

• Lectures on Generalized Symmetries
• Generalized global symmetries
• Introduction to Generalized Global Symmetries in QFT and Particle Physics
• ICTP Lectures on (Non-)Invertible Generalized Symmetries
• Generalised Symmetries in Particle Physics