Supersymmetry constraints on the R4 multiplet in type IIB string theory on T2

We consider a class of eight derivative interactions in the effective action of type IIB string theory compactified on T2. These 1/2 BPS interactions have moduli-dependent couplings. We impose the constraints of supersymmetry to show that each of these couplings satisfies a first order differential equation on moduli space which relate it to other couplings in the same supermuliplet. These equations can be iterated to give second order differential equations for the various couplings. The couplings which only depend on the SL(2,R4) moduli satisfy the Laplace equation on moduli space and are given by modular forms of SL(2,Z). On the other hand the ones that only depend on the SO(3), SL(3,R4) moduli satisfy the Poisson equation on moduli space where the source terms are given by other couplings in the same supermultiplet. The couplings of the interactions which are charged under SU(2) are not automorphic forms of SL(3,Z). Among the interactions that we consider the R4 coupling depends on all the moduli. (papers)