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Heterotic-string amplitudes at one loop: modular graph forms and relations to open strings

MPS-Authors
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Gerken,  Jan E.
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Kleinschmidt,  Axel
Quantum Gravity and Unified Theories, AEI Golm, MPI for Gravitational Physics, Max Planck Society;

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Schlotterer,  Oliver
Quantum Gravity and Unified Theories, AEI Golm, MPI for Gravitational Physics, Max Planck Society;

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1811.02548.pdf
(Preprint), 2MB

JHEP2019_052.pdf
(Publisher version), 2MB

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Citation

Gerken, J. E., Kleinschmidt, A., & Schlotterer, O. (2019). Heterotic-string amplitudes at one loop: modular graph forms and relations to open strings. Journal of high energy physics: JHEP, 2019(01): 52. doi:1007/JHEP01(2019)052.


Cite as: http://hdl.handle.net/21.11116/0000-0002-74EC-2
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.