Lax pairs for new \(\mathbb{Z}_N\)-symmetric coset \(\sigma\)-models and their Yang-Baxter deformations

DOI10.1016/j.nuclphysb.2022.115856zbMath1498.81107arXiv2112.07438OpenAlexW4281802314MaRDI QIDQ2155264

David Osten

Publication date: 15 July 2022

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

Full work available at URL: https://arxiv.org/abs/2112.07438

Mathematics Subject Classification ID

Supersymmetric field theories in quantum mechanics (81T60) Quantum field theory on curved space or space-time backgrounds (81T20) String and superstring theories; other extended objects (e.g., branes) in quantum field theory (81T30) Applications of Lie groups to the sciences; explicit representations (22E70) Kähler manifolds (32Q15) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Formal methods and deformations in algebraic geometry (14D15) Special quantum systems, such as solvable systems (81Q80)

Related Items

Bi-\(\eta\) and bi-\(\lambda\) deformations of \(\mathbb{Z}_4\) permutation supercosets ⋮ Universal 1-loop divergences for integrable sigma models

Cites Work

• Unnamed Item
• Scale invariance of the \(\eta\)-deformed \(\mathrm{AdS}_{5} \times S^{5}\) superstring, T-duality and modified type II equations
• Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory
• A Jordanian deformation of AdS space in type IIB supergravity
• Lunin-Maldacena backgrounds from the classical Yang-Baxter equation -- towards the gravity/CYBE correspondence
• Derivation of the action and symmetries of the \(q\)-deformed \({\mathrm{AdS}}_5\times S^5\) superstring
• Integrable deformations of strings on symmetric spaces
• Yang-Baxter sigma models based on the CYBE
• Hamiltonian dynamics and the hidden symmetries of the \(AdS_{5} \times S^{5}\) superstring
• The classical exchange algebra of \(AdS_{5} \times S^{5}\) string theory
• Superstrings on \(AdS_4\times\mathbb{CP}^3\) as a coset sigma-model
• Flat currents, \(\mathbb Z_m\) gradings and coset space actions
• Integrability of the bi-Yang-Baxter \(\sigma\)-model
• Abelian Yang-Baxter deformations and \(TsT\) transformations
• Cyclic gradings of Lie algebras and Lax pairs for \(\sigma\)-models
• Quantum reduction and representation theory of superconformal algebras
• Three-parameter integrable deformation of \(\mathbb Z_4\) permutation supercosets
• Supergravity backgrounds of the \(\eta\)-deformed \(\mathrm{AdS}_{2} \times S^2 \times T^6\) and \(\mathrm{AdS}_{5} \times S^5\) superstrings
• Yang-Baxter \(\sigma\)-model with WZNW term as \(\mathcal{E}\)-model
• On classical \(q\)-deformations of integrable \(\sigma\)-models
• Conformal sigma models on supercoset targets
• Towards a two-parameter \(q\)-deformation of \(\mathrm{AdS}_3 \times S^3 \times M^4\) superstrings
• Integrable double deformation of the principal chiral model
• Integrable properties of \(\sigma\) -models with non-symmetric target spaces
• On integrable deformations of superstring sigma models related to \(\mathrm{AdS}_n \times \mathrm{S}^n\) supercosets
• Green-Schwarz action for type IIA strings on \(AdS_{4}\times CP^{3}\)
• Type IIB superstring action in \(\text{AdS}_5\times S^5\) background
• \(\text{PSL}(n|n)\) sigma model as a conformal field theory
• Superstring theory on \(\text{AdS}_2\times S^2\) as a coset supermanifold
• Target space supergeometry of \(\eta\) and \(\lambda\)-deformed strings
• On the Hamiltonian integrability of the bi-Yang-Baxter \(\sigma\)-model
• Generalised fluxes, Yang-Baxter deformations and the O\((d,d)\) structure of non-abelian \(T\)-duality
• Local charges in involution and hierarchies in integrable sigma-models
• Combining the bi-Yang-Baxter deformation, the Wess-Zumino term and TsT transformations in one integrable \(\sigma\)-model
• Poisson-Lie duals of the \(\eta\) deformed symmetric space sigma model
• \(T\)-folds from Yang-Baxter deformations
• On non-abelian T-duality and deformations of supercoset string sigma-models
• Complex structures and zero-curvature equations for \(\sigma\)-models
• Non-Kähler string backgrounds and their five torsion classes
• Ultralocal Lax connection for para-complex \(\mathbb{Z}_T\)-cosets
• Automorphisms of finite order of semisimple Lie algebras
• Two-parameter integrable deformations of the \(\mathrm{AdS}_{3} \times S^3 \times T^4\) superstring
• Dressing cosets and multi-parametric integrable deformations
• Flag manifold $\sigma$-models: the $\frac{1}{N}$-expansion and the anomaly two-form
• Classification des variété Classification of homogeneous nearly Kähler manifolds approximativement Kähleriennes homogénes
• Affine and Riemannian s-manifolds
• Homogeneous spaces defined by Lie group automorphisms. II
• Nearly Kähler manifolds
• Type IIB supergravity solution for the T-dual of the \(\eta\)-deformed \(\mathrm{AdS}_{5}\times S^{5}\) superstring
• On jordanian deformations of AdS₅and supergravity
• Generalized type IIB supergravity equations and non-Abelian classicalr-matrices
• The classical exchange algebra of a Green-Schwarz sigma model on supercoset target space with $\mathbb {Z}_{4m}$Z4m grading
• Homogeneous Yang–Baxter deformations as non-abelian duals of theAdS₅σ-model
• On integrability of the Yang–Baxter σ-model
• Non-split and split deformations of ${\mathrm{AdS}}_{5}$
• The axial vector current in beta decay
• FLAT CURRENTS OF A GREEN–SCHWARZ SIGMA MODEL ON SUPERCOSET TARGETS WITH ℤ_4m GRADING
• AUTOMORPHISMS OF SIMPLE LIE SUPERALGEBRAS
• Conformal twists, Yang–Baxter σ-models & holographic noncommutativity
• Homogeneous Yang–Baxter deformations as generalized diffeomorphisms
• Marginal deformations of WZW models and the classical Yang–Baxter equation
• Harmonic Superspace
• Yang–Baxter deformations of the principal chiral model plus Wess–Zumino term
• Lie superalgebras
• \(\eta\) and \(\lambda\) deformations as \(\mathcal{E}\)-models