Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Affine Toda field theory as a 3-dimensional integrable system   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.

9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin