  The dual relationship between two n-1 parameter families of quantum field
theories based on extended complex numbers is investigated in two dimensions.
The non-local conserved charges approach is used. The lowest rank affine Toda
field theories are generated and identified as integrability submanifolds in
parameter space. A truncation of the model leads to a conformal field theory in
extended complex space. Depending on the projection over usual complex space
chosen, a parametrized central charge is calculated.
