Monodromy relations from twisted homology

Casali, Eduardo; Mizera, Sebastian; Tourkine, Piotr

doi:10.1007/JHEP12(2019)087

Title: Monodromy relations from twisted homology

Journal Article · 10 December 2019 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/JHEP12(2019)087 · OSTI ID:1597622

^[1]; Mizera, Sebastian ^[2]; Tourkine, Piotr ^[3]

Univ. of California, Davis, CA (United States); UC Davis
Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada); Univ. of Waterloo, ON (Canada); Inst. for Advanced Study, Princeton, NJ (United States)
Sorbonne Univ., Paris (France)

We reformulate the monodromy relations of open-string scattering amplitudes as boundary terms of twisted homologies on the configuration spaces of Riemann surfaces of arbitrary genus. This allows us to write explicit linear relations involving loop integrands of open-string theories for any number of external particles and, for the first time, to arbitrary genus. In the non-planar sector, these relations contain seemingly unphysical contributions, which we argue clarify mismatches in previous literature. The text is mostly self-contained and presents a concise introduction to twisted homologies. As a result of this powerful formulation, we can propose estimates on the number of independent loop integrands based on Euler characteristics of the relevant configuration spaces, leading to a higher-genus generalization of the famous (n - 3)! result at genus zero.

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Research Organization:: Univ. of California, Davis, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0009999

OSTI ID:: 1597622

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 12 Vol. 2019; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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