Non-Canonical Folding of Dynkin Diagrams and Reduction of Affine Toda Theories | Zendy

S. Pratik Khastgir | Zendy; Ryu Sasaki | Zendy

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Non-Canonical Folding of Dynkin Diagrams and Reduction of Affine Toda Theories

Author(s) -

S. Pratik Khastgir,

Ryu Sasaki

Publication year - 1996

Publication title -

progress of theoretical physics

Language(s) - English

Resource type - Journals

eISSN - 1347-4081

pISSN - 0033-068X

DOI - 10.1143/ptp.95.503

Subject(s) - dynkin diagram , affine transformation , rank (graph theory) , reduction (mathematics) , physics , symmetry (geometry) , lie algebra , pure mathematics , dimensional reduction , field (mathematics) , type (biology) , mathematics , mathematical physics , algebra over a field , theoretical physics , combinatorics , geometry , ecology , biology

The equation of motion of affine Toda field theory is a coupled equation for$r$ fields, $r$ is the rank of the underlying Lie algebra. Most of the theoriesadmit reduction, in which the equation is satisfied by fewer than $r$ fields.The reductions in the existing literature are achieved by identifying (folding)the points in the Dynkin diagrams which are connected by symmetry(automorphism). In this paper we present many new reductions. In other wordsthe symmetry of affine Dynkin diagrams could be extended and it leads tonon-canonical foldings. We investigate these reductions in detail and formulategeneral rules for possible reductions. We will show that eventually most of thetheories end up in $a_{2n}^{(2)}$ that is the theory cannot have a furtherdimension $m$ reduction where $m

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