Towards closed strings as single-valued open strings at genus one
Towards closed strings as single-valued open strings at genus one
We relate the low-energy expansions of world-sheet integrals in genus-one amplitudes of open- and closed-string states. The respective expansion coefficients are elliptic multiple zeta values (eMZVs) in the open-string case and non-holomorphic modular forms dubbed 'modular graph forms (MGFs)' for closed strings. By inspecting the differential equations and degeneration limits of suitable generating series of genus-one integrals, we identify formal substitution rules mapping the eMZVs of open strings to the MGFs of closed strings. Based on the properties of these rules, we refer to them as an elliptic single-valued map which generalizes the genus-zero notion of a single-valued map acting on MZVs seen in tree-level relations between the open and closed string.
elliptic integrals, modular forms, string amplitudes
Gerken, Jan E.
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Kleinschmidt, Axel
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Mafra, Carlos R.
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Schlotterer, Oliver
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Verbeek, Bram
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14 January 2022
Gerken, Jan E.
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Kleinschmidt, Axel
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Mafra, Carlos R.
5a40c14f-0ddb-4c0c-9ce5-acabc537cd01
Schlotterer, Oliver
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Verbeek, Bram
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Gerken, Jan E., Kleinschmidt, Axel, Mafra, Carlos R., Schlotterer, Oliver and Verbeek, Bram
(2022)
Towards closed strings as single-valued open strings at genus one.
Journal of Physics A: Mathematical and Theoretical, 55 (2), [025401].
(doi:10.1088/1751-8121/abe58b).
Abstract
We relate the low-energy expansions of world-sheet integrals in genus-one amplitudes of open- and closed-string states. The respective expansion coefficients are elliptic multiple zeta values (eMZVs) in the open-string case and non-holomorphic modular forms dubbed 'modular graph forms (MGFs)' for closed strings. By inspecting the differential equations and degeneration limits of suitable generating series of genus-one integrals, we identify formal substitution rules mapping the eMZVs of open strings to the MGFs of closed strings. Based on the properties of these rules, we refer to them as an elliptic single-valued map which generalizes the genus-zero notion of a single-valued map acting on MZVs seen in tree-level relations between the open and closed string.
Text
2010.10558v1
- Author's Original
More information
Submitted date: 20 October 2020
Accepted/In Press date: 11 February 2021
e-pub ahead of print date: 14 January 2022
Published date: 14 January 2022
Additional Information:
Publisher Copyright:
© 2021 The Author(s). Published by IOP Publishing Ltd.
Copyright:
Copyright 2022 Elsevier B.V., All rights reserved.
Keywords:
elliptic integrals, modular forms, string amplitudes
Identifiers
Local EPrints ID: 444876
URI: http://eprints.soton.ac.uk/id/eprint/444876
ISSN: 1751-8113
PURE UUID: e018bf0d-848c-4f39-acfe-f9ec3b967cc0
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Date deposited: 09 Nov 2020 17:30
Last modified: 06 Jun 2024 01:52
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Contributors
Author:
Jan E. Gerken
Author:
Axel Kleinschmidt
Author:
Oliver Schlotterer
Author:
Bram Verbeek
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