Abstract
In this short article we develop recent proposals to relate Yang-Baxter sigmamodels and non-abelian T-duality. We demonstrate explicitly that the holographic spacetimes associated to both (multi-parameter)-β-deformations and non-commutative deformations of mathcal{N} = 4 super Yang-Mills gauge theory including the RR fluxes can be obtained via the machinery of non-abelian T-duality in Type II supergravity.
Highlights
A new perspective on deformations of the AdS5 × S5 superstring has come from the study of Yang-Baxter deformations of string σ-models [8,9,10,11,12]
We demonstrate explicitly that the holographic spacetimes associated to both-β-deformations and non-commutative deformations of N = 4 super Yang-Mills gauge theory including the RR fluxes can be obtained via the machinery of non-abelian T-duality in Type II supergravity
Η-deformations are related via a generalised Poisson-Lie T-duality [18, 21,22,23,24,25] to a class of integrable deformation of WZW models known as λ-deformations [26,27,28], which do have target space-times solving the usual supergravity equations of motion [29,30,31,32]
Summary
We define an inner product by the matrix trace of generators, Tr(TATB), and lower and raise indices with this inner product and its inverse. In this way the r-matrix acts as. We introduce a projector to the coset defined by P (Tα) = 0 and P (Ti) = Ti or, in matrix form,. The standard (bosonic) σ-model whose target is the coset space F/G is. To define the Yang-Baxter model first we let Rg = Adg−1 R Adg , (Rg)AB = D(g)AC RC DD(g−1)DB ,. In which we have explicitly introduced the deformation parameter η. The Yang-Baxter σ-model on a coset is given by [15, 35].
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