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Explore the intricate connections between single-valued multiple zeta values and string amplitudes in this advanced mathematics lecture. Delve into the relationship between (N-3)-dimensional real iterated integrals on (RP1-{0,1,∞})N-3 and (N-3)-dimensional complex integrals on (CP1-{0,1,∞})N-3 through the single-valued map. Examine how these integrals relate to periods of the moduli space M0,N of genus zero curves with N ordered marked points. Discover the physical implications of these mathematical concepts, including the connection between tree-level open and closed string scattering amplitudes. Gain graphical insights into this relationship by analyzing beta-functions of two-dimensional sigma models describing world-sheets of open and closed (heterotic) strings. Investigate the sigma-model Feynman diagrams that generate identical effective action terms in both theories, and verify the single-valued map at the level of individual Feynman diagrams.
