The R-matrix of the U_q(d_4(3)) algebra and g_2(1) affine Toda field theory

TL;DR

This paper constructs the R-matrix for the U_q(d_4(3)) algebra, proposes an exact S-matrix for the g_2(1) affine Toda field theory, and explores its properties and special cases, including restrictions at roots of unity.

Contribution

It provides the explicit R-matrix in the fundamental representation and conjectures the exact S-matrix for the associated affine Toda field theory, linking algebraic structures to physical models.

Findings

R-matrix constructed for U_q(d_4(3)) algebra

Exact S-matrix conjectured for g_2(1) affine Toda theory

Consistency with real coupling and minimal model restrictions

Abstract

The R-matrix of the U_q(d_4(3)) algebra is constructed in the 8-dimensional fundamental representation. Using this result an exact S-matrix is conjectured for the imaginary coupled g_2(1) affine Toda field theory, the structure of which is found to be very similar to the previously investigated S-matrix of d_4(3) Toda theory. It is shown that this S-matrix is consistent with the results for the case of real coupling using the breather-particle correspondence. For q a root of unity it is argued that the theory can be restricted to yield Phi(11|12) perturbations of WA_2 minimal models.