Extended complex trigonometry in relation to integrable 2d-quantum field theories and duality

Multicomplex numbers of order n have an associated trigonometry (multisine functions with n−1 parameters) leading to a natural extension of the sine-Gordon model. The parameters are constrained from the requirement of local current conservation. In two dimensions for n<6 known integrable models (deformed Toda and non-linear sigma, pure affine Toda…) with dual counterparts are obtained in this way from the multicomplex space MCn itself and from the natural embedding MCn⊂MCm,n