Springer Berlin Heidelberg
Berlin/Heidelberg
Springer
13130
10.1007/13130.1029-8479
1029-8479
32745009
Journal of High Energy Physics
J. High Energ. Phys.
Physics
Elementary Particles, Quantum Field Theory
Quantum Field Theories, String Theory
Classical and Quantum Gravitation, Relativity Theory
Quantum Physics
Physics and Astronomy
2020
2020
12
7
7
244
2020
10
24
2020
7
2020
The Author(s)
2020
13475
2004.05156
10.1007/JHEP07(2020)190
190
190
Generating series of all modular graph forms from iterated Eisenstein integrals
Regular Article - Theoretical Physics
1
90
2020
7
27
2020
5
14
2020
6
24
2020
7
27
The Author(s)
2020
13130
2020
2020
7
7
Jan
E.
Gerken
jan.gerken@aei.mpg.de
Axel
Kleinschmidt
axel.kleinschmidt@aei.mpg.de
Oliver
Schlotterer
oliver.schlotterer@physics.uu.se
grid.450243.4
0000 0001 0790 4262
Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut
DE-14476
Potsdam
Germany
grid.425224.7
0000 0001 2189 8962
International Solvay Institutes ULB-Campus Plaine CP231
BE-1050
Brussels
Belgium
grid.8993.b
0000 0004 1936 9457
Department of Physics and Astronomy
Uppsala University
SE-75108
Uppsala
Sweden
Abstract
We study generating series of torus integrals that contain all so-called modular graph forms relevant for massless one-loop closed-string amplitudes. By analysing the differential equation of the generating series we construct a solution for their low-energy expansion to all orders in the inverse string tension α′. Our solution is expressed through initial data involving multiple zeta values and certain real-analytic functions of the modular parameter of the torus. These functions are built from real and imaginary parts of holomorphic iterated Eisenstein integrals and should be closely related to Brown’s recent construction of real-analytic modular forms. We study the properties of our real-analytic objects in detail and give explicit examples to a fixed order in the α′-expansion. In particular, our solution allows for a counting of linearly independent modular graph forms at a given weight, confirming previous partial results and giving predictions for higher, hitherto unexplored weights. It also sheds new light on the topic of uniform transcendentality of the α′-expansion.
Keywords
Conformal Field Models in String Theory
Scattering Amplitudes
Superstrings and Heterotic Strings
ArXiv ePrint:
2004.05156
Electronic supplementary material
The online version of this article (
https://doi.org/10.1007/JHEP07(2020)190
) contains supplementary material, which is available to authorized users.