Five-point Type IIB String Amplitudes at One Loop

TL;DR

This paper computes one-loop five-point amplitudes in type IIB superstring theory, revealing intricate mathematical structures and confirming duality constraints across different charge sectors.

Contribution

It provides the first detailed analysis of low-energy expansions of one-loop five-point amplitudes in all charge sectors, including novel interactions and mathematical structures.

Findings

Consistent with S-duality constraints

Reveals rich arithmetic structure including multiple zeta values

Identifies a new constant of unknown nature

Abstract

Massless type IIB superstring amplitudes are organized according to the number of external states and their ${\mathrm U}(1)$ charge under the R-symmetry of type IIB supergravity. In this work, we analyze the low-energy expansion of one-loop five-point amplitudes in all charge sectors, focusing on the representative processes involving five gravitons and four gravitons with one dilaton. We compute the one-loop contributions to the moduli-dependent couplings in the type IIB effective action up to the $D^{12}R^5$ and $D^{14}\phi R^4$ interactions. The results are consistent with $S$-duality constraints in every charge sector and exhibit rich arithmetic structure, including single-valued multiple zeta values, affine linear combinations of logarithmic derivatives of the Riemann zeta function at odd integers, and a new constant of currently unknown nature.