On the Witten–Duff five Branes model together with knots theory and E8E8 super strings in a single fractal spacetime theory

The Witten–Duff five Branes in 11 dimensions model which leads to N = 528 states is reviewed. A complimentary model leading to N = 496 of E8E8 exceptional Lie symmetry group is established along identical ideas. Subsequently both models are combined into a general one which includes the zero-form missing in the original five Branes model. Finally a highly instructive connection to jE12j = 685 Lie symmetry group which encompasses E11 as well as the number of distinct knots for given crossing numbers is established. It is concluded that it is easier to transfinitely extend the five Branes model than to add additional roots of exceptional Lie groups in order to find the exact answer.