Motivic Multiple Zeta Values and Superstring Amplitudes

The structure of tree–level open and closed superstring amplitudes is analyzed. For the open superstring amplitude we find a striking and elegant form, which allows to disentangle its α–expansion into several contributions accounting for different classes of multiple zeta values. This form is bolstered by the decomposition of motivic multiple zeta values, i.e. the latter encapsulate the α–expansion of the superstring amplitude. Moreover, a morphism induced by the coproduct maps the α–expansion onto a non–commutative Hopf algebra. This map represents a generalization of the symbol of a transcendental function. In terms of elements of this Hopf algebra the α–expansion assumes a very simple and symmetric form, which carries all the relevant information. Equipped with these results we can also cast the closed superstring amplitude into a very elegant form.