Abstract
We investigate one-loop four-point scattering of non-abelian gauge bosons in heterotic string theory and identify new connections with the corresponding open-string amplitude. In the low-energy expansion of the heterotic-string amplitude, the integrals over torus punctures are systematically evaluated in terms of modular graph forms, certain non-holomorphic modular forms. For a specific torus integral, the modular graph forms in the low-energy expansion are related to the elliptic multiple zeta values from the analogous open-string integrations over cylinder boundaries. The detailed correspondence between these modular graph forms and elliptic multiple zeta values supports a recent proposal for an elliptic generalization of the single-valued map at genus zero.
Highlights
Scattering amplitudes in string theories have become a rewarding laboratory to encounter modern number-theoretic concepts in a simple setup
We investigate one-loop four-point scattering of non-abelian gauge bosons in heterotic string theory and identify new connections with the corresponding open-string amplitude
The detailed correspondence between these modular graph forms and elliptic multiple zeta values supports a recent proposal for an elliptic generalization of the single-valued map at genus zero
Summary
Scattering amplitudes in string theories have become a rewarding laboratory to encounter modern number-theoretic concepts in a simple setup. By comparing the eMZVs and modular graph functions in one-loop amplitudes of open and closed strings, a conjecture for the explicit form of an elliptic singlevalued map has been made in [22]. Given that the heterotic string relaxes the maximal supersymmetry of type-II superstrings, its extended set of moduli-space integrals (as investigated here at four points) is hoped to give a more general picture of an elliptic single-valued map As another consequence of the half-maximal supersymmetry of the heterotic string, the coefficients of a given modular graph form in massless one-loop amplitudes usually mix different orders in α. Relating an integral of modular weight (2, 0) in the four-point gauge amplitude of the heterotic string to a cylinder integral of the open superstring by applying the tentative elliptic single-valued map of [22] order by order in the α -expansion. Several technical details needed in the analysis have been relegated to a number of appendices
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
