Abstract
In the low-energy effective action of string theories, non-abelian gauge interactions and supergravity are augmented by infinite towers of higher-mass-dimension operators. We propose a new method to construct one-loop matrix elements with insertions of operators D2kFn and D2kRn in the tree-level effective action of type-I and type-II superstrings. Inspired by ambitwistor string theories, our method is based on forward limits of moduli-space integrals using string tree-level amplitudes with two extra points, expanded in powers of the inverse string tension α′. Similar to one-loop ambitwistor computations, intermediate steps feature non-standard linearized Feynman propagators which eventually recombine to conventional quadratic propagators. With linearized propagators the loop integrand of the matrix elements obey one-loop versions of the monodromy and KLT relations. We express a variety of four- and five-point examples in terms of quadratic propagators and formulate a criterion on the underlying genus-one correlation functions that should make this recombination possible at all orders in α′. The ultraviolet divergences of the one-loop matrix elements are crosschecked against the non-separating degeneration of genus-one integrals in string amplitudes. Conversely, our results can be used as a constructive method to determine degenerations of elliptic multiple zeta values and modular graph forms at arbitrary weight.
Highlights
Recent years have witnessed remarkable synergies between properties and building blocks of massless string amplitudes and new structures of field-theory amplitudes
A central example is the double-copy structure of perturbative gravity [1,2,3], which is manifest in the Kawai-Lewellen-Tye open/closed string relations [4], the chiral-splitting description of string amplitudes [5, 6], and kinematic numerators in multiloop field-theory amplitudes [2, 7, 8]
As another line of motivation, the one-loop matrix elements in this work serve as testing grounds whether large numbers of loop momenta in the numerator can be reconciled with the color-kinematics duality [1, 2]
Summary
Recent years have witnessed remarkable synergies between properties and building blocks of massless string amplitudes and new structures of field-theory amplitudes. The matrix elements of this work do not fix the analytic contributions to one-loop string amplitudes, i.e. the terms with powerseries behaviour in the Mandelstam variables Such analytic terms and the associated loop corrections to the superstring effective actions (1.1) can be thought of as partially originating from purely massive loop integrals, which have no branch cuts below the ultraviolet (UV) cutoff of the effective field theory. They are beyond the reach of the computations in this work since all the propagators in the α -expansion of our one-loop matrix elements (see e.g. figure 1) refer to massless states
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