Dressing cosets revisited

We present an alternative algebraic derivation of the dual pair of nonlinear $\sigma$-models based on the 'dressing cosets' extension of the Poisson-Lie $T$-duality \cite{KS1}. Then we generalize the result to dual pairs of Lagrangians not considered in \cite{KS1}. Our generalization turns out to incorporate the dualisable models constructed by Sfetsos in \cite{Sfet1}.Comment: 24 page

Lunin-Maldacena backgrounds from the classical Yang-Baxter equation -- Towards the gravity/CYBE correspondence

We consider \gamma-deformations of the AdS_5xS^5 superstring as Yang-Baxter sigma models with classical r-matrices satisfying the classical Yang-Baxter equation (CYBE). An essential point is that the classical r-matrices are composed of Cartan generators only and then generate abelian twists. We present examples of the r-matrices that lead to real \gamma-deformations of the AdS_5xS^5 superstring. Finally we discuss a possible classification of integrable deformations and the corresponding gravity solution in terms of solutions of CYBE. This classification may be called the gravity/CYBE correspondence.Comment: 18 pages, no figure, LaTeX, v2:references and further clarifications adde

Grand symmetry, spectral action and the Higgs mass

In the context of the spectral action and the noncommutative geometry approach to the standard model, we build a model based on a larger symmetry. With this grand symmetry it is natural to have the scalar field necessary to obtain the Higgs mass in the vicinity of 126 GeV. This larger symmetry mixes gauge and spin degrees of freedom without introducing extra fermions. Requiring the noncommutative space to be an almost commutative geometry (i.e. the product of manifold by a finite dimensional internal space) gives conditions for the breaking of this grand symmetry to the standard model. \ua9 2014 SISSA