Closed string amplitudes from single-valued correlation functions

Pierre Vanhove (1) , Federico Zerbini (1)

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681

We argue in two different ways that the low-energy expansion of any tree-level closed string amplitudes only involves single-valued multiple zeta values. First, we identify the building blocks of any closed string amplitudes with the value at $z=1$ of single-valued correlation functions in two dimensional conformal field theory. We use the single-valuedness condition to determine uniquely the correlation function and determine the role of the momentum kernel in the single-valued projection. The second argument is more technical and leads to a mathematical proof of the statement. It is obtained through a direct analysis of the $\alpha'$-expansion of closed string integrals, whose coefficients are given by multiple integrals of single-valued hyperlogarithms over the complex plane. The main new tool is the extension to the single-valued case of some technical results used for multiple integration of holomorphic hyperlogarithms.

Domaines: Physique des Hautes Energies - Théorie [hep-th]; Physique des Hautes Energies - Phénoménologie [hep-ph]; Physique mathématique [math-ph]; Cosmologie et astrophysique extra-galactique [astro-ph.CO]; Physique mathématique [math-ph]; Théorie des nombres [math.NT]

Pierre Vanhove, Federico Zerbini. Closed string amplitudes from single-valued correlation functions. Advances in Theoretical and Mathematical Physics, 2022, 26 (2), pp.455-530. ⟨10.4310/ATMP.2022.v26.n2.a5⟩. ⟨hal-01956505⟩