The two D6R4 type invariants and their higher order generalisation

Understand

We show that there are two distinct classes of D6R4 type supersymmetry invariants in maximal supergravity.

• The second class includes a coupling in F2D4R4 that generalises to 1/8 BPS protected F2kD4R4 couplings.
• We work out the supersymmetry constraints on the corresponding threshold functions, and argue that the functions in the second class satisfy to homogeneous differential equations for arbitrary k>0, such that the corresponding exact threshold functions in type II string theory should be proportional to Eisenstein series, which we identify.
• This analysis explains in particular that the exact D6R4 threshold function is the sum of an Eisenstein function and a solution to an inhomogeneous Poisson equation in string theory.