All Jordanian deformations of the $Ad{S}_5\times S^5$ superstring

Abstract

We explicitly construct and classify all Jordanian solutions of the classical Yang-Baxter equation on $\mathfrak{psu}(2,2|4)$, corresponding to Jordanian Yang-Baxter deformations of the $Ad{S}_5\times S^5$ superstring. Such deformations preserve the classical integrability of the underlying sigma-model and thus are a subclass of all possible integrable deformations. The deformations that we consider are divided into two families, unimodular and non-unimodular ones. The former ensure that the deformed backgrounds are still solutions of the type IIB supergravity equations. For the simplest unimodular solutions, we find that the corresponding backgrounds preserve a number $N<32$ of supercharges that can be $N=12,8,6,4,0$.

39 pages, 2 appendices, many tables, v2: expanded conclusions, missing unimodular R_6 solutions included, updated discussion on so(6) shifts, various minor changes to address the referee reports

References in corpus (14)

• Target space supergeometry of $\eta$ and $\lambda$-deformed strings
• An Integrable Deformation of the AdS5 x S5 Superstring
• Abelian Yang-Baxter Deformations and TsT transformations
• Integrable Deformations of Strings on Symmetric Spaces
• Yang-Baxter sigma models based on the CYBE
• Spacetimes for λ-deformations
• Kappa-symmetry of superstring sigma model and generalized 10d supergravity equations
• Homogeneous Yang-Baxter deformations as non-abelian duals of the AdS_5 sigma-model
• Integrable Deformations of Sigma Models
• Unimodular jordanian deformations of integrable superstrings
• Homogeneous Yang-Baxter deformations as undeformed yet twisted models
• Semiclassical spectrum of a Jordanian deformation of $Ad{S}_5\times S^5$
• An Algebraic Classification of Solution Generating Techniques
• Quadratic twist-noncommutative gauge theory

Cited by in corpus (2)

• Yang-Baxter structure of the extended space
• Jordanian spin chains for twisted strings in $Ad{S}_5\times S^5$