More on (gauged) WZW models over low-dimensional Lie supergroups and their integrable deformations

Abstract

In superdimension $(2|2)$ there are only three non-Abelian Lie superalgebras admitting non-degenerate ad-invariant supersymmetric metric, the well-known Lie superalgebra $gl(1|1)$, and two more, $({\C}^3 + \A)$ and $({\C}_0^5 +{\A})$. After a brief review of the construction of the Wess-Zumino-Witten (WZW) models based on the $GL(1|1)$ and $(C^3+A)$ Lie supergroups, we proceed to construct the WZW model on the $(C_0^5+A)$ Lie supergroup. Unfortunately, this model does not include the super Poisson-Lie symmetry. In the following, three new exact conformal field theories of the WZW type are constructed by gauging an anomaly-free subgroup SO(2) of the Lie supergroups mentioned above. The most interesting indication of this work is that the gauged WZW model on the supercoset $(C^3+A)/$SO(2) has super Poisson-Lie symmetry; most importantly, its dual model is conformally invariant at the one-loop order, and this is presented here for the first time. Finally, in order to study the Yang-Baxter (YB) deformations of the $(C_0^5+A)$ WZW model we obtain the inequivalent solutions of the (modified) graded classical Yang-Baxter equation ((m)GCYBE) for the $({\C}_0^5 +{\A})$ Lie superalgebra. Then, we classify all possible YB deformations for the $(C_0^5+A)$ and settle also the issue of an one-loop conformality of the deformed backgrounds. The classification results are important, in particular in the Lie supergroup case they are rare, much hard technical work was needed to obtain them.

arXiv comment39 pages, to appear in Fortschr. Phys

References in corpus (89)

• Type IIB superstring action in AdS_5 x S^5 background
• On integrability of the Yang-Baxter $\si$-model
• An integrable deformation of the AdS_5 x S^5 superstring action
• A WZW model based on a non-semi-simple group
• Dual Non-Abelian Duality and the Drinfeld Double
• Yang-Baxter $\sigma$-models and dS/AdS T-duality
• On classical q-deformations of integrable sigma-models
• Conformal Field Theory of AdS Background with Ramond-Ramond Flux
• Green-Schwarz action for Type IIA strings on $Ad{S}_4\times C{P}^3$
• Superstring Theory on AdS_2 x S^2 as a Coset Supermanifold
• Superstrings on AdS_4 x CP^3 as a Coset Sigma-model
• Exact Black String Solutions in Three Dimensions
• Derivation of the action and symmetries of the q-deformed AdS_5 x S^5 superstring
• S-matrix for strings on $\eta$-deformed AdS5 x S5
• Scale invariance of the eta-deformed AdS5 x S5 superstring, T-duality and modified type II equations
• Jordanian deformations of the AdS_5xS^5 superstring
• Poisson-Lie T-duality
• On Non-Abelian Duality
• A Local Logarithmic Conformal Field Theory
• Target space supergeometry of $\eta$ and $\lambda$-deformed strings
• gl(N|N) Super-Current Algebras for Disordered Dirac Fermions in Two Dimensions
• Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory
• Abelian Yang-Baxter Deformations and TsT transformations
• The GL(1|1) WZW model: From Supergeometry to Logarithmic CFT
• Exact Duality Symmetries in CFT and String Theory
• Non-unitary Conformal Field Theory and Logarithmic Operators for Disordered Systems
• $PSL(n|n)$ Sigma Model as a Conformal Field Theory
• Marginal Deformations of WZNW and Coset Models from O(d,d) Transformation
• Strings on Curved Spacetimes: Black Holes, Torsion, and Duality
• Kappa-symmetry of superstring sigma model and generalized 10d supergravity equations
• Integrable double deformation of the principal chiral model
• Nonsemisimple Sugawara Constructions
• A Large Class of New Gravitational and Axionic Backgrounds for Four-Dimensional Superstrings
• A Jordanian deformation of AdS space in type IIB supergravity
• A Class of String Backgrounds as a Semiclassical Limit of WZW Models
• S and T matrices for the super $U(1,1)$ WZW model. Application to surgery and 3-manifold invariants based on the Alexander Conway polynomial
• Homogeneous Yang-Baxter deformations as non-abelian duals of the AdS_5 sigma-model
• Superstring Gravitational Wave Backgrounds with Spacetime Supersymmetry
• The WZNW model on PSU(1,1|2)
• Gauging a Non-Semi-Simple WZW Model
• Non-abelian T-duality and Yang-Baxter deformations of Green-Schwarz strings
• Finite sigma models and exact string solutions with Minkowski signature metric
• Quantum Poisson-Lie T-duality and WZNW model
• Generalised fluxes, Yang-Baxter deformations and the O(d,d) structure of non-abelian T-duality
• On Bosonic and Supersymmetric Current Algebras for Non-Semi-Simple Groups
• Exact string background from a WZW model based on the Heisenberg group
• Conformal Twists, Yang-Baxter $\sigma$-models & Holographic Noncommutativity
• Conformal Sigma-Models on Supercoset Targets
• Free fermion resolution of supergroup WZNW models
• Branes in the GL(1|1) WZNW-Model
• Yang-Baxter $\sigma$-model with WZNW term as $\mathcal{E}$-model
• Exact string backgrounds from WZW models based on non-semi-simple groups
• Superspace conformal field theory
• Conformal invariance and quantum integrability of sigma models on symmetric superspaces
• Yang-Baxter deformations of the Principal Chiral Model plus Wess-Zumino term
• Unimodular jordanian deformations of integrable superstrings
• Classical and Quantum Aspects of Yang-Baxter Wess-Zumino Models
• Chiral Gauged WZW Theories and Coset Models in Conformal Field Theory
• Poisson-Lie T-dual sigma models on supermanifolds
• Yang-Baxter invariance of the Nappi-Witten model
• Classification of Low Dimensional Lie Super-Bialgebras
• Integrable asymmetric $\lambda$-deformations
• BTZ black hole from Poisson-Lie T-dualizable sigma models with spectators
• Classification of two and three dimensional Lie super-bialgebras
• Super Poisson-Lie symmetry of the GL(1|1) WZNW model and worldsheet boundary conditions
• Exact conformal field theories from mutually T-dualizable $\sigma$-models
• Poisson Lie symmetry and D-branes in WZW model on the Heisenberg Lie group $H_4$
• Yang-Baxter deformations and generalized supergravity -- A short summary
• String cosmology from Poisson-Lie T-dual sigma models on supermanifolds
• Abelian duality in WZW models
• Strong integrability of the bi-YB-WZ model
• The abelian cosets of the Heisenberg group
• WZW models as mutual super Poisson-Lie T-dual sigma models
• Super Non-Abelian T-Duality
• Classification of four and six dimensional Drinfel'd superdoubles
• Generalized Dualities and Supergroups
• The gl(1|1) Lie superbialgebras
• Conformal superspace sigma-models
• The diagonal cosets of the Heisenberg group
• Yang-Baxter deformations of WZW model on the Heisenberg Lie group
• Classical r-matrices of two and three dimensional Lie super-bialgebras and their Poisson-Lie supergroups
• Yang-Baxter deformation of WZW model based on Lie supergroups: The cases of $GL(1|1)$ and $(C^3+A)$
• Non-chiral current algebras for deformed supergroup WZW models
• A hierarchy of WZW models related to super Poisson-Lie T-duality
• Lie superbialgebra structures on the Lie superalgebra $({\mathcal{C}}^3+\mathcal{A})$ and deformation of related integrable Hamiltonian systems
• Yang-Baxter deformations of the $GL(2,\mathbb{R})$ WZW model and non-Abelian T-duality
• $Ad{S}_3\times S^3$ Background from Poisson-Lie T-Duality
• Wess-Zumino-Witten Model for Galilean Conformal Algebra
• Non-relativistic quantum strings from gauged WZW models

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• Integrable sigma models with Haantjes structure on $H_4$ Lie group