Gauged WZW-type theories and the all-loop anisotropic non-Abelian Thirring model

Abstract

We study what we call the all-loop anisotropic bosonized Thirring sigma model. This interpolates between the WZW model and the non-Abelian T-dual of the principal chiral model for a simple group. It has an invariance involving the inversion of the matrix parametrizing the coupling constants. We compute the general renormalization group flow equations which assume a remarkably simple form and derive its properties. For symmetric couplings, they consistently truncate to previous results in the literature. One of the examples we provide gives rise to a first order system of differential equations interpolating between the Lagrange and the Darboux-Halphen integrable systems.

1+25 pages, Latex, v2: 1+26 pages, Latex. Added comments regarding fixed points of the two coupling case, NPB version, v3: Front page corrected, v4: Correcting a typo in Eq. (8.1)

References in corpus (2)

• Integrable interpolations: From exact CFTs to non-Abelian T-duals
• The all-loop non-Abelian Thirring model and its RG flow

Cited by in corpus (51)

• An Integrable Deformation of the AdS5 x S5 Superstring
• Integrable Deformations of Strings on Symmetric Spaces
• Spacetimes for λ-deformations
• Beta Function of k Deformed AdS_5 x S^5 String Theory
• Integrable Deformations of Sigma Models
• Integrable flows between exact CFTs
• The classical Yang-Baxter equation and the associated Yangian symmetry of gauged WZW-type theories
• $\lambda$-deformations of left-right asymmetric CFTs
• S-Matrices and Quantum Group Symmetry of k-Deformed Sigma Models
• All-loop anomalous dimensions in integrable $\lambda$-deformed $\sigma$-models
• All-loop correlators of integrable $\lambda$-deformed $\sigma$-models
• Double and cyclic $\lambda$-deformations and their canonical equivalents
• Integrable deformations of the $G_{k_1}\times G_{k_2}/G_{k_1+k_2}$ coset CFTs
• The anisotropic λ-deformed SU(2) model is integrable
• The most general $\lambda$-deformation of CFTs and integrability
• Integrable sigma models and 2-loop RG flow
• Novel all loop actions of interacting CFTs: Construction, integrability and RG flows
• A new class of integrable deformations of CFTs
• Quantum aspects of doubly deformed CFTs
• RG flows of integrable $\sigma$-models and the twist function
• Integrable asymmetric $\lambda$-deformations
• RG flows for $\lambda$-deformed CFTs
• Sigma models with local couplings: a new integrability -- RG flow connection
• An exact symmetry in $\lambda$-deformed CFTs
• The exact $C$-function in integrable $\lambda$-deformed theories
• Quantum Inverse Scattering and the Lambda Deformed Principal Chiral Model
• Yang Baxter and Anisotropic Sigma and Lambda Models, Cyclic RG and Exact S-Matrices
• Quantum Anisotropic Sigma and Lambda Models as Spin Chains
• Weyl anomaly and the $C$-function in $\lambda$-deformed CFTs
• Universal 1-loop divergences for integrable sigma models
• Exploring The Lambda Model Of The Hybrid Superstring
• Integrability vs. RG flow in $G\times G$ and $G\times G/H$ sigma models
• Exact results from the geometry of couplings and the effective action
• Geometry of the spectral parameter and renormalisation of integrable $\sigma$-models
• Deformed WZW Models and Hodge Theory -- Part I
• Peculiarities of beta functions in sigma models
• Novel integrable interpolations
• Webs of integrable theories
• Hamiltonian integrability of the webs of integrable theories
• Asymptotics in an Asymptotic CFT
• Integrable $\lambda$-deformations of the Euclidean black string
• Integrable Lorentz-breaking deformations and RG flows
• $\lambda$-deformations in the upper-half plane
• A free field perspective of $\lambda$-deformed coset CFT's
• Scattering in integrable pp-wave backgrounds: S-matrix and absence of particle production
• Integrability of the $\lambda$-deformation of the PCM with spectators
• Scale without conformal invariance from integrable deformations of coset CFTs
• Integrable models based on non-semi-simple groups and plane wave target spacetimes
• Integrability and renormalizability for the fully anisotropic $\mathrm{SU}(2)$ principal chiral field and its deformations
• A generalized method for all-loop results in $\lambda$-models
• Kerr-Schild perturbations of coset CFTs as scale invariant integrable $\sigma$-models