Abstract
We show that there are two distinct classes of ∇6R4 type supersymmetry invariants in maximal supergravity. The second class includes a coupling in F2∇4R4 that generalises to 1/8 BPS protected F2k∇4R4 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 ≥ 1, 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 ∇6R4 threshold function is the sum of an Eisenstein function and a solution to an inhomogeneous Poisson equation in string theory.
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Bossard, G., Verschinin, V. The two ∇6R4 type invariants and their higher order generalisation. J. High Energ. Phys. 2015, 154 (2015). https://doi.org/10.1007/JHEP07(2015)154
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DOI: https://doi.org/10.1007/JHEP07(2015)154