Single-valued hyperlogarithms, correlation functions and closed string amplitudes

We give new proofs of a global and local property the integrals which compute closed string theory amplitudes at genus zero. Both kinds properties are related to newborn single-valued periods, our provide an intuitive understanding this relation. The property, known in physics as KLT formula, is factorisation into products pairs open integrals. deduce it by identifying with special values correlation functions two dimensional conformal field theory, obtaining their block decomposition. number theoretical nature. write asymptotic expansion coefficients multiple over complex plane hyperlogarithms. develop integration hyperlogarithms, we use demonstrate that belong ring zeta values.