Classical and Quantum Aspects of Yang-Baxter Wess-Zumino Models

Abstract

We investigate the integrable Yang-Baxter deformation of the 2d Principal Chiral Model with a Wess-Zumino term. For arbitrary groups, the one-loop beta functions are calculated and display a surprising connection between classical and quantum physics: the classical integrability condition is necessary to prevent new couplings being generated by renormalisation. We show these theories admit an elegant realisation of Poisson-Lie T-duality acting as a simple inversion of coupling constants. The self-dual point corresponds to the Wess-Zumino-Witten model and is the IR fixed point under RG. We address the possibility of having supersymmetric extensions of these models showing that extended supersymmetry is not possible in general.

44 pages; 4 figures; v2: references added; v3: published version, text edited and restructured, result added on CFT operators driving the flow

References in corpus (18)

• On space of integrable quantum field theories
• Target space supergeometry of $\eta$ and $\lambda$-deformed strings
• An Integrable Deformation of the AdS5 x S5 Superstring
• Integrable Deformations of Strings on Symmetric Spaces
• Spacetimes for λ-deformations
• Yangian symmetry in deformed WZNW models on squashed spheres
• Supergravity background of the lambda-deformed AdS_3 x S^3 supercoset
• Hidden Yangian symmetry in sigma model on squashed sphere
• $T$-folds from Yang-Baxter deformations
• Yang-Baxter $\sigma$-model with WZNW term as $\mathcal{E}$-model
• $I$ in generalized supergravity
• Combining the bi-Yang-Baxter deformation, the Wess-Zumino term and TsT transformations in one integrable sigma-model
• Irreversibility of the renormalization group flow in non-unitary quantum field theory
• Integrable deformations of the $G_{k_1}\times G_{k_2}/G_{k_1+k_2}$ coset CFTs
• Poisson-Lie duals of the eta deformed symmetric space sigma model
• Generalized $\lambda$-deformations of AdS_p x S^p
• On integrability of 2-dimensional $\sigma$-models of Poisson-Lie type
• Yang Baxter and Anisotropic Sigma and Lambda Models, Cyclic RG and Exact S-Matrices

Cited by in corpus (28)

• Doubled aspects of generalised dualities and integrable deformations
• Integrable Deformations of Sigma Models
• A unifying 2d action for integrable $\sigma$-models from 4d Chern-Simons theory
• Yang-Baxter Deformations Beyond Coset Spaces (a slick way to do TsT)
• Local $\beta$-deformations and Yang-Baxter sigma model
• Yang-Baxter deformations of the Principal Chiral Model plus Wess-Zumino term
• Dressing cosets and multi-parametric integrable deformations
• Introduction to classical and quantum integrability
• Para-Hermitian Geometries for Poisson-Lie Symmetric $\sigma$-models
• Three-parameter integrable deformation of Z_4 permutation supercosets
• RG flows of integrable $\sigma$-models and the twist function
• Integrable deformations of coupled sigma-models
• Brief lectures on duality, integrability and deformations
• Integrable supersymmetric deformations of $\mathrm{Ad}{\mathrm{S}}_3\times {\mathrm{S}}^3\times {\mathrm{T}}^4$
• Strong integrability of the bi-YB-WZ model
• D-branes in $\lambda$-deformations
• Quantum Anisotropic Sigma and Lambda Models as Spin Chains
• Integrability vs. RG flow in $G\times G$ and $G\times G/H$ sigma models
• Probing analytical and numerical integrability: The curious case of $(Ad{S}_5\times S^5{)}_{\eta }$
• On strong integrability of the dressing cosets
• The Magic Renormalisability of Affine Gaudin Models
• On some integrable deformations of the Wess-Zumino-Witten model
• Yang-Baxter deformations of the $GL(2,\mathbb{R})$ WZW model and non-Abelian T-duality
• On a class of conformal $\mathcal{E}$-models and their chiral Poisson algebras
• Sigma model on a squashed sphere with a Wess-Zumino term
• Separation of variables in the WZW models
• More on (gauged) WZW models over low-dimensional Lie supergroups and their integrable deformations
• Yang-Baxter deformations of the OSP(1|2) WZW model