One-loop matrix elements of effective superstring interactions: ??-expanding loop integrands

A bstract In the low-energy effective action of string theories, non-abelian gauge interactions and supergravity are augmented by infinite towers higher-mass-dimension operators. We propose a new method to construct one-loop matrix elements with insertions operators D 2 k F n R in tree-level type-I type-II superstrings. Inspired ambitwistor our is based on forward limits moduli-space integrals using amplitudes two extra points, expanded powers inverse tension ?? . Similar computations, intermediate steps feature non-standard linearized Feynman propagators which eventually recombine conventional quadratic propagators. With loop integrand obey versions monodromy KLT relations. express variety four- five-point examples terms formulate criterion underlying genus-one correlation functions that should make this recombination possible at all orders The ultraviolet divergences crosschecked against non-separating degeneration amplitudes. Conversely, results can be used as constructive determine degenerations elliptic multiple zeta values modular graph forms arbitrary weight.