Yang Baxter and Anisotropic Sigma and Lambda Models, Cyclic RG and Exact S-Matrices

Abstract

Integrable deformation of SU(2) sigma and lambda models are considered at the classical and quantum levels. These are the Yang-Baxter and XXZ-type anisotropic deformations. The XXZ type deformations are UV safe in one regime, while in another regime, like the Yang-Baxter deformations, they exhibit cyclic RG behaviour. The associated affine quantum group symmetry, realized classically at the Poisson bracket level, has q a complex phase in the UV safe regime and q real in the cyclic RG regime, where q is an RG invariant. Based on the symmetries and RG flow we propose exact factorizable S-matrices to describe the scattering of states in the lambda models, from which the sigma models follow by taking a limit and non-abelian T-duality. In the cyclic RG regimes, the S-matrices are periodic functions of rapidity, at large rapidity, and in the Yang-Baxter case violate parity.

55 pages; v2 - refs added and some expanded discussion of \tildeβ^ϕ

References in corpus (30)

• On integrability of the Yang-Baxter $\si$-model
• An integrable deformation of the AdS_5 x S^5 superstring action
• Yang-Baxter $\sigma$-models and dS/AdS T-duality
• On classical q-deformations of integrable sigma-models
• Integrable interpolations: From exact CFTs to non-Abelian T-duals
• Derivation of the action and symmetries of the q-deformed AdS_5 x S^5 superstring
• On deformations of AdS_n x S^n supercosets
• Integrability of the bi-Yang-Baxter sigma-model
• Generalised integrable $\lambda$- and $\eta$-deformations and their relation
• Introduction to Yangian symmetry in integrable field theory
• Non-Abelian Duality and Canonical Transformations
• Quantizing SL(N) Solitons and the Hecke Alegbra
• Hybrid classical integrability in squashed sigma models
• The classical origin of quantum affine algebra in squashed sigma models
• Gauged WZW-type theories and the all-loop anisotropic non-Abelian Thirring model
• On sigma model RG flow, "central charge" action and Perelman's entropy
• Principal Chiral Field at Large N
• On the classical equivalence of monodromy matrices in squashed sigma model
• On the Beta Function for Anisotropic Current Interactions in 2D
• On a `universal' class of WZW-type conformal models
• Russian Doll Renormalization Group, Kosterlitz-Thouless Flows, and the Cyclic sine-Gordon model
• Log-periodic behavior of finite size effects in field theories with RG limit cycles
• Integrable theories that are asymptotically CFT
• RG flows, cycles, and c-theorem folklore
• The anisotropic λ-deformed SU(2) model is integrable
• The exact mass-gaps of the principal chiral models
• Strong-weak coupling duality in anisotropic current interactions
• Affine q-deformed symmetry and the classical Yang-Baxter sigma-model
• Renormalization group limit-cycles and field theories for elliptic S-matrices
• A Quantum Field Theory with Infinite Resonance States

Cited by in corpus (10)

• Integrable Deformations of Sigma Models
• Integrable flows between exact CFTs
• Yang-Baxter Deformations Beyond Coset Spaces (a slick way to do TsT)
• Classical and Quantum Aspects of Yang-Baxter Wess-Zumino Models
• Ultralocal Lax connection for para-complex ${\mathbb{Z}}_T$-cosets
• Quantum Anisotropic Sigma and Lambda Models as Spin Chains
• Probing analytical and numerical integrability: The curious case of $(Ad{S}_5\times S^5{)}_{\eta }$
• An elliptic integrable deformation of the Principal Chiral Model
• Integrability and renormalizability for the fully anisotropic $\mathrm{SU}(2)$ principal chiral field and its deformations
• On dual regime in Yang-Baxter deformed $\mathrm{O}(2N)$ sigma models