Type II superstring amplitude at one-loop and transcendentality

Abstract

We calculate the four-graviton scattering amplitude in Type II superstring theory at one loop up to seventh order in the low-energy expansion through the recently developed iterated integral formalism of Modular Graph Functions (MGFs). The machinery of the novel method allows us to propose a general form of the amplitude, which suggests that the expansion is expressible in terms of single-valued multiple zeta values and logarithmic derivatives of the Riemann zeta function at positive and negative odd integers. Furthermore, we comment on the transcendental behavior of the amplitude.

6 pages; Submission includes ancillary data file; v3: Sections rearranged and minor changes - version appeared in PRL

References in corpus (9)

• All-order differential equations for one-loop closed-string integrals and modular graph forms
• Generating series of all modular graph forms from iterated Eisenstein integrals
• Tetrahedral modular graph functions
• Poincaré series for modular graph forms at depth two. II. Iterated integrals of cusp forms
• Poincaré series for modular graph forms at depth two. I. Seeds and Laplace systems
• Modular graph forms from equivariant iterated Eisenstein integrals
• Integrating three-loop modular graph functions and transcendentality of string amplitudes
• Non-analytic terms of string amplitudes from partial waves
• Integral of depth zero to three basis of Modular Graph Functions

Cited by in corpus (2)

• From Modular Graph Forms to Iterated Integrals
• One-loop four-graviton string amplitude at finite ${\alpha }^{\prime }$