Flag manifold $\sigma$-models: the $\frac{1}{N}$-expansion and the anomaly two-form

DOI10.1016/j.nuclphysb.2019.02.006zbMath1415.81035arXiv1901.02861OpenAlexW2949176076MaRDI QIDQ2421484

Dmitri Bykov

Publication date: 17 June 2019

Published in: Nuclear Physics. B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.02861

Mathematics Subject Classification ID

Model quantum field theories (81T10) Grassmannians, Schubert varieties, flag manifolds (14M15) Yang-Mills and other gauge theories in quantum field theory (81T13) Anomalies in quantum field theory (81T50) Symmetries and conservation laws in mechanics of particles and systems (70S10)

Related Items

Flag manifold sigma models. Spin chains and integrable theories, Quantum cohomology of symplectic flag manifolds, Lax pairs for new \(\mathbb{Z}_N\)-symmetric coset \(\sigma\)-models and their Yang-Baxter deformations, Ultralocal Lax connection for para-complex \(\mathbb{Z}_T\)-cosets, Ricci-flat metrics on vector bundles over flag manifolds, Flag manifold sigma models and nilpotent orbits, Quantum flag manifold \(\sigma \)-models \textit{and} Hermitian Ricci flow, Dressing cosets and multi-parametric integrable deformations

Cites Work

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• Classical solutions of a flag manifold \(\sigma\)-model
• The geometry of antiferromagnetic spin chains
• Flat currents, \(\mathbb Z_m\) gradings and coset space actions
• Cyclic gradings of Lie algebras and Lax pairs for \(\sigma\)-models
• Haldane limits via Lagrangian embeddings
• Integrable properties of \(\sigma\) -models with non-symmetric target spaces
• Quantization of symplectic orbits of compact Lie groups by means of the functional integral
• GLSMs for partial flag manifolds
• Tournaments, flags, and harmonic maps
• Integrable nonlinear \(\sigma\) models with fermions
• Harmonic maps into Lie groups (classical solutions of the chiral model)
• Hidden Yangians in 2D massive current algebras
• On the Hamiltonian integrability of the bi-Yang-Baxter \(\sigma\)-model
• Generalization of the Haldane conjecture to \(\operatorname{SU}(3)\) chains
• Complex structure-induced deformations of \(\sigma\)-models
• A gauged linear formulation for flag-manifold \(\sigma\)-models
• Multiparticle \(\mathcal{N} = 8\) mechanics with \(F(4)\) superconformal symmetry
• Complex structures and zero-curvature equations for \(\sigma\)-models
• Integrable Hamiltonian systems and interactions through quadratic constraints
• The sigma model (dual) representation for a two-parameter family of integrable quantum field theories
• Automorphisms of finite order of semisimple Lie algebras
• Harmonic maps from a 2-torus to the 3-sphere
• Construction of Lax connections by exponentiation
• On integrability of the Yang–Baxter σ-model
• Characteristic Classes and Homogeneous Spaces, I
• The Hamiltonian formalism and a many-valued analogue of Morse theory
• Unconstrained off-shell N=3 supersymmetric Yang-Mills theory
• Minimal coupling and the symplectic mechanics of a classical particle in the presence of a Yang-Mills field
• Constrained affine Gaudin models and diagonal Yang–Baxter deformations
• Lectures on Nakajima's Quiver Varieties