Towards closed strings as single-valued open strings at genus one
Artikel i vetenskaplig tidskrift, 2022

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

string amplitudes

modular forms


Jan Gerken

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Algebra och geometri

Axel Kleinschmidt


Université libre de Bruxelles (ULB)

Carlos R. Mafra

University of Southampton

Oliver Schlotterer

Uppsala universitet

Bram Verbeek

Uppsala universitet

Journal of Physics A: Mathematical and Theoretical

1751-8113 (ISSN) 1751-8121 (eISSN)

Vol. 55 2 025401


Algebra och logik


Matematisk analys



Mer information

Senast uppdaterat