Motivic Superstring Amplitudes
Seminar Room 1, Newton Institute
We review the recent advances in open superstring N-point tree-level computations. One basic ingredient is a basis of (N-3)! generalized Gaussian hypergeometric functions (generalized Euler integrals) encoding all string effects through their dependence on the string tension $\alpha'$. The structure of the open superstring amplitudes is analyzed. We find a striking and elegant form, which allows to disentangle its $\alpha'$ power series 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 $\alpha'$-expansion of the superstring amplitude. Moreover, a morphism induced by the coproduct maps the $\alpha'$-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 alpha'-expansion assumes a very simple and symmetric form, which carries all the relevant information.