Non-canonical folding of Dynkin diagrams and reduction of affine Toda theories

Details Non-canonical folding of Dynkin diagrams and reduction of affine Toda theories Non-canonical folding of Dynkin diagrams and reduction of affine Toda theories

1995-12-20

arxiv.org/abs/hep-th/9512158v1

Prog.Theor.Phys. 95 (1996) 503-518

Physics

High Energy Physics

High Energy Physics - Theory

26 pages, Latex2e, usepackage `graphics.sty', 15 figures

Scientific paper

10.1143/PTP.95.503

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 theories admit 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 words the symmetry of affine Dynkin diagrams could be extended and it leads to non-canonical foldings. We investigate these reductions in detail and formulate general rules for possible reductions. We will show that eventually most of the theories end up in $a_{2n}^{(2)}$ that is the theory cannot have a further dimension $m$ reduction where $m

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