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

Abstract : 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.
Document type :
Journal articles

https://hal.archives-ouvertes.fr/hal-00019439
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Submitted on : Tuesday, February 21, 2006 - 8:31:57 PM
Last modification on : Tuesday, August 2, 2022 - 3:48:28 AM

### Citation

P. Baseilhac, S. Galice, P. Grangé, M. Rausch de Traubenberg. Extended Complex Trigonometry in Relation to Integrable 2D-Quantum Field Theories and Duality. Physics Letters B, Elsevier, 2000, 478, pp.365-372. ⟨hal-00019439⟩

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