# R**4 couplings and automorphic unipotent representations

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 matching the infinitesimal characters, and from the fact that the Fourier coefficients have support on 1/2-BPS charges. 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 $\nabla^4 R^4$ couplings in dimensions D=3,4,5.
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Journal articles
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https://hal.archives-ouvertes.fr/hal-00449200
Contributor : Boris Pioline Connect in order to contact the contributor
Submitted on : Thursday, January 21, 2010 - 9:06:26 AM
Last modification on : Tuesday, November 16, 2021 - 4:54:35 AM

### Identifiers

• HAL Id : hal-00449200, version 1
• ARXIV : 1001.3647

### Citation

Boris Pioline. R**4 couplings and automorphic unipotent representations. Journal of High Energy Physics, Springer, 2010, pp.JHEP03(2010)116. ⟨hal-00449200⟩

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