The two ∇6 R 4 type invariants and their higher order generalisation
Abstract
We show that there are two distinct classes of ∇6 R 4 type supersymmetry invariants in maximal supergravity. The second class includes a coupling in F 2∇4 R 4 that generalises to 1/8 BPS protected F 2 k ∇4 R 4 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 ∇6 R 4 threshold function is the sum of an Eisenstein function and a solution to an inhomogeneous Poisson equation in string theory.
- Publication:
-
Journal of High Energy Physics
- Pub Date:
- July 2015
- DOI:
- 10.1007/JHEP07(2015)154
- arXiv:
- arXiv:1503.04230
- Bibcode:
- 2015JHEP...07..154B
- Keywords:
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- Extended Supersymmetry;
- Nonperturbative Effects;
- Supergravity Models;
- Supersymmetric Effective Theories;
- High Energy Physics - Theory
- E-Print:
- 53 pages