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#### Towards closed strings as single-valued open strings at genus one

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2010.10558.pdf

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Gerken_2022_J._Phys._A _Math._Theor._55_025401.pdf

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##### Citation

Gerken, J. E., Kleinschmidt, A., Mafra, C. R., Schlotterer, O., & Verbeek, B. (2022).
Towards closed strings as single-valued open strings at genus one.* Journal of Physics A,*
*55*(2): 025401. doi:10.1088/1751-8121/abe58b.

Cite as: https://hdl.handle.net/21.11116/0000-0007-62C3-E

##### 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 in the open-string case and

non-holomorphic modular forms dubbed "modular graph forms" 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 elliptic multiple zeta values of open strings to the modular graph

forms 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 multiple zeta values seen in tree-level

relations between the open and closed string.

amplitudes of open- and closed-string states. The respective expansion

coefficients are elliptic multiple zeta values in the open-string case and

non-holomorphic modular forms dubbed "modular graph forms" 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 elliptic multiple zeta values of open strings to the modular graph

forms 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 multiple zeta values seen in tree-level

relations between the open and closed string.