Supersymmetry constraints on the R^4 multiplet in type IIB on T^2

Understand

We consider a class of eight derivative interactions in the effective action of type IIB string theory compactified on T^2.

• These 1/2 BPS interactions have moduli dependent couplings.
• We impose the constraints of supersymmetry to show that each of these couplings satisfy 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.