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Title: Monodromy relations from twisted homology

Abstract

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.

Authors:
ORCiD logo [1];  [2];  [3]
+ Show Author Affiliations
  1. Univ. of California, Davis, CA (United States)
  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)
Publication Date:
Research Org.:
Univ. of California, Davis, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1597622
Grant/Contract Number:  
[SC0009999]
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
[Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2019; Journal Issue: 12]; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats

Casali, Eduardo, Mizera, Sebastian, and Tourkine, Piotr. Monodromy relations from twisted homology. United States: N. p., 2019. Web. doi:10.1007/JHEP12(2019)087.
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Casali, Eduardo, Mizera, Sebastian, & Tourkine, Piotr. Monodromy relations from twisted homology. United States. doi:10.1007/JHEP12(2019)087.
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Casali, Eduardo, Mizera, Sebastian, and Tourkine, Piotr. Wed . "Monodromy relations from twisted homology". United States. doi:10.1007/JHEP12(2019)087. https://www.osti.gov/servlets/purl/1597622.
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@article{osti_1597622,
title = {Monodromy relations from twisted homology},
author = {Casali, Eduardo and Mizera, Sebastian and Tourkine, Piotr},
abstractNote = {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.},
doi = {10.1007/JHEP12(2019)087},
journal = {Journal of High Energy Physics (Online)},
number = [12],
volume = [2019],
place = {United States},
year = {2019},
month = {12}
}
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DOI:  10.1007/JHEP12(2019)087
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