Study of gapped phases of 4d gauge theories using temporal gauging of the ${\mathbb{Z}}_N$ 1-form symmetry

Abstract

To study gapped phases of $4$d gauge theories, we introduce the temporal gauging of ${\mathbb{Z}}_N$ $1$-form symmetry in $4$d quantum field theories (QFTs), thereby defining effective $3$d QFTs with ${\tilde{\mathbb{Z}}}_N\times {\mathbb{Z}}_N$ $1$-form symmetry. In this way, spatial fundamental Wilson and 't Hooft loops are simultaneously genuine line operators. Assuming a mass gap and Lorentz invariant vacuum of the $4$d QFT, the ${\tilde{\mathbb{Z}}}_N\times {\mathbb{Z}}_N$ symmetry must be spontaneously broken to an order-$N$ subgroup $H$, and we can classify the $4$d gapped phases by specifying $H$. This establishes the $1$-to-$1$ correspondence between the two classification schemes for gapped phases of $4$d gauge theories: One is the conventional Wilson-'t Hooft classification, and the other is the modern classification using the spontaneous breaking of $4$d $1$-form symmetry enriched with symmetry-protected topological states.

arXiv comment23 pages, 2 figures; (v2) refs added, fixed typos

References in corpus (25)

• Generalized Global Symmetries
• A Strong Coupling Test of S-Duality
• Supersymmetric Yang-Mills Systems And Integrable Systems
• Coupling a QFT to a TQFT and Duality
• Reading between the lines of four-dimensional gauge theories
• Theta, Time Reversal, and Temperature
• Exploring 2-Group Global Symmetries
• On gauging finite subgroups
• On Mirror Symmetry in Three Dimensional Abelian Gauge Theories
• Anomalies in the Space of Coupling Constants and Their Dynamical Applications II
• On the classification of topological orders
• Notes on generalized global symmetries in QFT
• An Elliptic Superpotential for Softly Broken N=4 Supersymmetric Yang-Mills Theory
• Anomaly constraints on deconfinement and chiral phase transition
• A classification of 3+1D bosonic topological orders (I): the case when point-like excitations are all bosons
• Modified instanton sum in QCD and higher-groups
• Anomaly matching for phase diagram of massless ${\mathbb{Z}}_N$-QCD
• Non-invertible self-duality defects of Cardy-Rabinovici model and mixed gravitational anomaly
• Vacuum structure of bifundamental gauge theories at finite topological angles
• Circle compactification and 't Hooft anomaly
• Higher-form symmetries and 3-group in axion electrodynamics
• Global 3-group symmetry and 't Hooft anomalies in axion electrodynamics
• The Bi-Fundamental Gauge Theory in 3+1 Dimensions: The Vacuum Structure and a Cascade
• TQFT, Symmetry Breaking, and Finite Gauge Theory in 3+1D
• Topological aspects of $4$D Abelian lattice gauge theories with the $\theta$ parameter

Cited by in corpus (4)

• Generating Lattice Non-invertible Symmetries
• Twisted Partition Functions as Order Parameters
• Center-vortex semiclassics with non-minimal 't Hooft fluxes on ${\mathbb{R}}^2\times T^2$ and center stabilization at large $N$
• Tensor renormalization group approach to critical phenomena via symmetry-twisted partition functions