S-matrices of non-simply laced affine Toda theories by folding

Abstract The exact factorisable quantum S -matrices are known for simply laced as well as non-simply laced affine Toda field theories. Non-simply laced theories are obtained from the affine Toda theories based on simply laced algebras by folding the corresponding Dynkin diagrams. The same process, called classical ‘reduction’, provides solutions of a non-simply laced theory from the classical solutions with special symmetries of the parent simply laced theory. In the present note we shall elevate the idea of folding and classical reduction to the quantum level. To support our views we have made some interesting observations for S -matrices of non-simply laced theories and give a prescription for obtaining them through the folding of simply laced ones.