Higher-derivative couplings in string theory: five-point contact terms

TL;DR

The paper addresses higher-derivative corrections in type II string theory by deriving the tree-level $H^2R^3$ couplings from the five-point amplitude and constructing a quintic action that includes both standard $t_8t_8R(\Omega_+)^4$-type terms and novel $H^2R^3$ structures. It demonstrates that tree-level kinematics contain new contributions such as $t_8t_8H^2R(\Omega_+)^3$ and $\epsilon_9\epsilon_9H^2R(\Omega_+)^3$, which differ from the one-loop results, and tests these couplings via reductions on K3 and CY manifolds. The K3 reductions reveal cancellations governed by six-dimensional SUSY, while CY reductions tie the ten-dimensional action to moduli-space corrections in 4D ${\cal N}=2$ theories, highlighting intricate SUSY and duality constraints. The work points to a richer non-linear invariant structure in the NSNS and RR sectors, with implications for $SL(2,\mathbb Z)$ duality, RR couplings, and potential underlying geometric principles guiding higher-derivative string interactions.

Abstract

We compute the tree-level $H^2R^3$ couplings of type II strings and provide some basic tests of the couplings by considering both K3 and Calabi-Yau threefold compactifications. Curiously, additional kinematical structures show up at tree level that are not present in the one-loop couplings. This has interesting implications for type II supersymmetry as well as $SL(2, \mathbb Z)$ duality in type IIB strings.