https://hal-cnrs.archives-ouvertes.fr/hal-03852548Bianchi, MassimoMassimoBianchiBossard, GuillaumeGuillaumeBossardCPHT - Centre de Physique Théorique [Palaiseau] - X - École polytechnique - CNRS - Centre National de la Recherche ScientifiqueConsoli, DarioDarioConsoliPerturbative higher-derivative terms in N = 6 asymmetric orbifoldsHAL CCSD2022[PHYS.HTHE] Physics [physics]/High Energy Physics - Theory [hep-th]Bossard, Guillaume2022-11-15 09:45:322022-11-16 03:46:272022-11-15 09:45:32enJournal articles10.1007/JHEP06(2022)0881We 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.