Perturbative higher-derivative terms in N=6 asymmetric orbifolds

TL;DR

This paper investigates four-point amplitudes in N=6 supersymmetric string theory backgrounds, revealing symmetry properties, supersymmetry constraints, and conjectures about U-duality and non-perturbative effects.

Contribution

It introduces the analysis of perturbative amplitudes in asymmetric orbifold models with N=6 supersymmetry and proposes a conjecture for the U-duality group and non-perturbative completions.

Findings

Amplitude invariance under arithmetic symplectic groups

Determination of supersymmetry constraints on couplings

Conjecture of U-duality group and non-perturbative theta series

Abstract

We analyse the perturbative four-point amplitudes in the simplest string theory examples of T-fold backgrounds, which enjoy N=6 supersymmetries in four dimensions. There are two theories defined as asymmetric orbifolds of order 2 and 3, respectively. The perturbative spectrum and the one-loop four-point amplitudes are shown to be invariant under an arithmetic symplectic group defined over the Hurwitz (respectively Eisenstein) quaternions. The supersymmetry constraints on the low energy effective couplings are determined and we conjecture the U-duality group of the theory and the non-perturbative completion of the six-derivative coupling as a rank one theta series. We discuss the non-perturbative spectrum of BPS states in the light of our analysis.