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