Yang-Baxter deformations of the OSP(1|2) WZW model

Abstract

We obtain inequivalent classical r-matrices of the $osp(1|2)$ Lie superalgebra as real solutions of the graded (modified) classical Yang-Baxter equation, in such a way that the corresponding automorphism transformation is employed. Then, Yang-Baxter deformations of the Wess-Zumino-Witten model based on the OSP$(1|2)$ Lie supergroup are specified by super skew-symmetric classical r-matrices. In this regard, the effect coming from the deformation is reflected as the coefficient of both metric and $B$-field. Furthermore, it is shown that all resulting classical r-matrices are non-Abelian and also non-unimodular, which leads us to graded generalized supergravity equations. We show that the background of undeformed model is a solution of the graded generalized supergravity equations when supplemented by an appropriate supervector field obtaining from the linear combination of the Killing supervectors corresponding to the background, while the deformed models do not satisfy these equations. This is consistent with our expectations, since the deformed models under consideration do not describe a Green-Schwarz superstring. However, the deformed backgrounds are interesting, in particular in the OSP$(1|2)$ case they are rare, much hard technical work was needed to obtain them.

19 pages

References in corpus (14)

• Derivation of the action and symmetries of the q-deformed AdS_5 x S^5 superstring
• Target space supergeometry of $\eta$ and $\lambda$-deformed strings
• Abelian Yang-Baxter Deformations and TsT transformations
• Kappa-symmetry of superstring sigma model and generalized 10d supergravity equations
• Yang-Baxter $\sigma$-model with WZNW term as $\mathcal{E}$-model
• Generalized type IIB supergravity equations and non-Abelian classical r-matrices
• Yang-Baxter deformations of the Principal Chiral Model plus Wess-Zumino term
• Structure constants of the OSP(1|2) WZNW model
• Unimodular jordanian deformations of integrable superstrings
• Poisson-Lie T-dual sigma models on supermanifolds
• Super Non-Abelian T-Duality
• Yang-Baxter deformation of WZW model based on Lie supergroups: The cases of $GL(1|1)$ and $(C^3+A)$
• Yang-Baxter deformations of the $GL(2,\mathbb{R})$ WZW model and non-Abelian T-duality
• Integrable sigma models with complex and generalized complex structures

Cited by in corpus (1)

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