The R-matrix of the Uq( d4(3)) algebra and g2(1) affine Toda field theory

Abstract

The R-matrix of the Uq( 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 Φ(11‖12) perturbations of WA 2 minimal models.