Extended Complex Trigonometry in Relation to Integrable 2D-Quantum Field Theories and Duality

Baseilhac, P.; Galice, S.; Grangé, P.; de Traubenberg, M. Rausch

Extended Complex Trigonometry in Relation to Integrable 2D-Quantum Field Theories and Duality

Authors

Baseilhac, P.

Galice, S.

Grangé, P.

de Traubenberg, M. Rausch

Description

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 MC itself and from the natural embedding $\MC_n \subset \MMC_m, n < m$. For $ n \ge 6$ a generic constraint on the space of parametersis obtained from current conservation at first order in the interaction Lagragien.
11 pages, no figure, LaTex with amsmath accepted by Phys. Lett. B