Dihedral symmetry in $SU(N)$ Yang-Mills theory

Abstract

We point out that charge conjugation and coordinate reflection symmetries do not commute with the center symmetry of $SU(N)$ YM theory when $N>2$. As a result, for generic values of the $\theta$ angle, the group of discrete zero-form symmetries of YM theory on e.g. the spacetime manifold ${\mathbb{R}}^3\times S^1$ includes the dihedral group $D_{2N}$ which is non-Abelian for $N>2$. At $\theta =\pi$, the non-Abelian factor in the symmetry group is enhanced to $D_{4N}$ due to discrete 't Hooft anomaly considerations. We illustrate these results in YM theory as well as in a simple quantum mechanical model, where we study representation theory as a function of $\theta$ angle.

31 pages, 3 figures. v2: added refs and minor typos fixed

References in corpus (24)

• Generalized Global Symmetries
• Symmetries and Strings in Field Theory and Gravity
• Exploring 2-Group Global Symmetries
• Center-stabilized Yang-Mills theory: confinement and large $N$ volume independence
• Magnetic bion condensation: A new mechanism of confinement and mass gap in four dimensions
• On 2-Group Global Symmetries and Their Anomalies
• Higher-Dimensional Algebra V: 2-Groups
• Abelian duality, confinement, and chiral symmetry breaking in QCD(adj)
• Finite size phase transitions in QCD with adjoint fermions
• Vacuum structure of bifundamental gauge theories at finite topological angles
• Adjoint QCD on ${\mathbb{R}}^3\times S^1$ with twisted fermionic boundary conditions
• Phase diagrams of SU(N) gauge theories with fermions in various representations
• Deconfinement and continuity between thermal and (super) Yang-Mills theory for all gauge groups
• Global inconsistency, 't Hooft anomaly, and level crossing in quantum mechanics
• Large-N reduction in QCD-like theories with massive adjoint fermions
• QCD on a small circle
• On Yang-Mills Theories with Chiral Matter at Strong Coupling
• Compactified N=1 supersymmetric Yang-Mills theory on the lattice: Continuity and the disappearance of the deconfinement transition
• Metastable vacuum decay and $\theta$ dependence in gauge theory. Deformed QCD as a toy model
• Oblique Confinement at $\theta \ne 0$ in weakly coupled gauge theories with deformations
• Vacuum structure of Yang-Mills theory as a function of $\theta$
• On the representation (in)dependence of $k$-strings in pure Yang-Mills theory via supersymmetry
• New nonperturbative scales and glueballs in confining supersymmetric gauge theories
• Metastable vacuum decay in center-stabilized Yang-Mills theory at large N

Cited by in corpus (12)

• Symmetries and Strings of Adjoint QCD${}_2$
• Anomaly matching, (axial) Schwinger models, and high-T super Yang-Mills domain walls
• Anomalies, a mod 2 index, and dynamics of 2d adjoint QCD
• Lifetimes of (near) eternal false vacua
• Notes on Confinement on ${\mathbf{R}}^3\times {\mathbf{S}}^1$: From Yang-Mills, super-Yang-Mills, and QCD(adj) to QCD(F)
• Topological aspects of $4$D Abelian lattice gauge theories with the $\theta$ parameter
• New Anomalies, TQFTs, and Confinement in Bosonic Chiral Gauge Theories
• Gauge theory geography: charting a path between semiclassical islands
• Domain Walls in 4d N=1 Supersymmetric Yang-Mills
• C-P-T Fractionalization
• Topological terms and anomaly matching in effective field theories on ${\mathbb{R}}^3\times S^1$: I. Abelian symmetries and intermediate scales
• The mixed $0$-form/$1$-form anomaly in Hilbert space: pouring new wine into old bottles