arXiv subjects
Publications and source records attributed to Romain Squellari.
We study the quantum properties at one-loop of the Yang-Baxter $σ$-models introduced by Klimč\'\ik. The proof of the one-loop renormalizability is given, the one-loop renormalization flow is investigated and the quantum equivalence is studied.
We present an alternative algebraic derivation of the dual pair of nonlinear $σ$-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}.
We will present a new extension of the standard model of particle physics in its almostcommutative formulation. This extension has as its basis the algebra of the standard model with four summands [11], and enlarges only the particle content by an arbitrary number of generations of left-right symmetric doublets which couple vectorially to the U(1)_YxSU(2)_w subgroup of the standard model. As in the model presented in [8], which introduced particles with a new colour, grand unification is no longer required by the spectral action. The new model may also possess a candidate for dark matter in the hundred TeV mass range with neutrino-like cross section.