Affine Toda Field Theory as a 3Dimensional Integrable System
Abstract
The affine Toda field theory is studied as a 2+1dimensional 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. The quantum analog of the τvariables is found. The thermodynamic Bethe ansatz of the affine Toda system is studied in the limit L,N>∞. It is shown that the free energy of the systems grows proportionally to the volume.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 1997
 DOI:
 10.1007/s002200050164
 arXiv:
 arXiv:hepth/9507065
 Bibcode:
 1997CMaPh.188..251K
 Keywords:

 High Energy Physics  Theory
 EPrint:
 17 pages, LaTeX