Affine Toda field theory as a 3-dimensional integrable system

Details Affine Toda field theory as a 3-dimensional integrable system Affine Toda field theory as a 3-dimensional integrable system

1995-07-11

arxiv.org/abs/hep-th/9507065v1

Commun.Math.Phys. 188 (1997) 251-266

Physics

High Energy Physics

High Energy Physics - Theory

17 pages, LaTeX

Scientific paper

10.1007/s002200050164

The affine Toda field theory is studied as a 2+1-dimensional system. The third dimension appears as the discrete space dimension, corresponding to the simple roots in the $A_N$ affine root system, enumerated according to the cyclic order on the $A_N$ affine Dynkin diagram. We show that there exists a natural discretization of the affine Toda theory, where the equations of motion are invariant with respect to permutations of all discrete coordinates. The discrete evolution operator is constructed explicitly. The thermodynamic Bethe ansatz of the affine Toda system is studied in the limit $L,N\to\infty$. Some conjectures about the structure of the spectrum of the corresponding discrete models are stated.

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