Abstract
Four-graviton, eight-derivative couplings in the low energy effective action of toroidal type II string compactifications are tightly constrained by U-duality invariance and by supersymmetry. In this note, we revisit earlier proposals for the automorphic form governing these couplings in dimension D = 3, 4, 5, 6, and propose that the correct automorphic form is the minimal theta series for the corresponding U-duality group. Evidence for this proposal comes from i) the matching of infinitesimal characters, ii) the fact that the Fourier coefficients have support on 1/2-BPS charges and iii) decompactification limits. In particular, we show that non-perturbative effects can be interpreted as 1/2-BPS instantons, or 1/2-BPS particles in one dimension higher (together with Taub-NUT instantons in the D = 3 case). Based on similar considerations, we also conjecture the form of 1/4-BPS saturated couplings such as ∇4 R 4 couplings in the same dimensions.
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Pioline, B. R4 couplings and automorphic unipotent representations. J. High Energ. Phys. 2010, 116 (2010). https://doi.org/10.1007/JHEP03(2010)116
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DOI: https://doi.org/10.1007/JHEP03(2010)116