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Title: Monodromy relations from twisted homology

Journal Article · · Journal of High Energy Physics (Online)
ORCiD logo [1];  [2];  [3]
  1. Univ. of California, Davis, CA (United States); UC Davis
  2. Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada); Univ. of Waterloo, ON (Canada); Inst. for Advanced Study, Princeton, NJ (United States)
  3. 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.

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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Cited By (2)

All-order differential equations for one-loop closed-string integrals and modular graph forms text January 2019
All-order differential equations for one-loop closed-string integrals and modular graph forms journal January 2020

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