Double-Copy Structure of One-Loop Open-String Amplitudes

TL;DR

Evidence is provided for a new double-copy structure in one-loop amplitudes of the open superstring where gauge-invariant kinematic factors and certain functions of the punctures-so-called generalized elliptic integrands-enter on completely symmetric footing.

Abstract

In this Letter, we provide evidence for a new double-copy structure in one-loop amplitudes of the open superstring. Their integrands with respect to the moduli space of genus-one surfaces are cast into a form where gauge-invariant kinematic factors and certain functions of the punctures -- so-called generalized elliptic integrands -- enter on completely symmetric footing. In particular, replacing the generalized elliptic integrands by a second copy of kinematic factors maps one-loop open-string correlators to gravitational matrix elements of the higher-curvature operator R^4.

Figures (1)

• Figure 1: Parameterization of a torus as a lattice $\mathbb C/(\mathbb Z{+}\tau \mathbb Z)$ with discrete identifications $z \cong z{+}1 \cong z{+}\tau$ of the punctures and modular parameter $\tau$ in the upper half plane.