On affine Toda field theories related to D _r algebras and their real Hamiltonian forms

Abstract The paper deals with affine 2-dimensional Toda field theories related to simple Lie algebras of the classical series D r . We demonstrate that the complexification procedure followed by a restriction to a specified real Hamiltonian form commutes with the external automorphisms of 𝔤. This is illustrated on the examples D r + 1 ( 1 ) → B r ( 1 ) and D 4 ( 1 ) → G 2 ( 1 ) using external automorphisms of the corresponding extended Dynkin diagrams.