Topological terms of (2+1)d flag-manifold sigma models

Abstract

We examine topological terms of $(2+1)$d sigma models and their consequences in the light of classifications of invertible quantum field theories utilizing bordism groups. In particular, we study the possible topological terms for the $U(N)/U(1{)}^N$ flag-manifold sigma model in detail. We argue that the Hopf-like term is absent, contrary to the expectation from a nontrivial homotopy group ${\pi }_3(U(N)/U(1{)}^N)=\mathbb{Z}$, and thus skyrmions cannot become anyons with arbitrary statistics. Instead, we find that there exist $\frac{N(N-1)}{2}-1$ types of Chern-Simons terms, some of which can turn skyrmions into fermions, and we write down explicit forms of effective Lagrangians.

arXiv comment29 pages; (v2) minor changes, refs updated

References in corpus (32)

• Topological Field Theory of Time-Reversal Invariant Insulators
• Two-orbital SU(N) magnetism with ultracold alkaline-earth atoms
• Spectroscopic observation of SU(N)-symmetric interactions in Sr orbital magnetism
• An SU(N) Mott insulator of an atomic Fermi gas realized by large-spin Pomeranchuk cooling
• Ultracold Fermi Gases with Emergent SU(N) Symmetry
• Ultracold fermions and the SU(N) Hubbard model
• Ultracold Gases of Ytterbium: Ferromagnetism and Mott States in an SU(6) Fermi System
• Topological Disorder Operators in Three-Dimensional Conformal Field Theory
• Spin Nematic Phase in S=1 Triangular Antiferromagnets
• Reflection positivity and invertible topological phases
• Theta-terms in nonlinear sigma-models
• Partial duality in SU(N) Yang-Mills theory
• Setting the quantum integrand of M-theory
• Phases of one-dimensional SU(N) cold atomic Fermi gases --from molecular Luttinger liquids to topological phases
• Anomaly and global inconsistency matching: $\theta$-angles, $SU(3)/U(1{)}^2$ nonlinear sigma model, $SU(3)$ chains and its generalizations
• Waves in the unseen : theory of spin excitations in a quantum spin nematic
• On the cobordism classification of symmetry protected topological phases
• Generalization of the Haldane conjecture to SU(3) chains
• Floquet chiral magnetic effect
• The Sum Over Topological Sectors and $\theta$ in the 2+1-Dimensional $\mathbb{C}{\mathbb{P}}^1$ $\sigma$-Model
• Haldane limits via Lagrangian embeddings
• Revisiting Wess-Zumino-Witten terms
• Sigma Models on Flags
• The geometry of antiferromagnetic spin chains
• General anomaly matching by Goldstone bosons
• Classical solutions of a flag manifold sigma-model
• Phase structure of the twisted $SU(3)/U(1{)}^2$ flag sigma model on $\mathbb{R}\times S^1$
• Hopf term induced by fermions
• $SU(3)$ Knot Solitons: Hopfions in the $F_2$ Skyrme-Faddeev-Niemi model
• Topological Terms and Phases of Sigma Models
• Flag manifold sigma models from SU($n$) chains
• Deconfined quantum criticality in SU(3) antiferromagnets on the triangular lattice

Cited by in corpus (4)

• Solitonic symmetry beyond homotopy: Invertibility from bordism and noninvertibility from topological quantum field theory
• Topological continuum charges of acoustic phonons in 2D
• Theory of topological defects and textures in two-dimensional quantum orders with spontaneous symmetry breaking
• Sigma-model analysis of $SU(3)$ antiferromagnetic spins on the triangular lattice