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Journal Article

Cancellation of divergences up to three loops in exceptional field theory

MPS-Authors
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Bossard,  Guillaume
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Kleinschmidt,  Axel
Quantum Gravity and Unified Theories, AEI Golm, MPI for Gravitational Physics, Max Planck Society;

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Fulltext (public)

1712.02793.pdf
(Preprint), 485KB

JHEP03(2018)100.pdf
(Publisher version), 569KB

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Citation

Bossard, G., & Kleinschmidt, A. (2018). Cancellation of divergences up to three loops in exceptional field theory. Journal of High Energy Physics, 2018(03): 100. doi:10.1007/JHEP03(2018)100.


Cite as: http://hdl.handle.net/11858/00-001M-0000-002E-9AF1-B
Abstract
We consider the tetrahedral three-loop diagram in $E_d$ exceptional field theory evaluated as a scalar diagram for four external gravitons. At lowest order in momenta, this diagram contributes to the $\nabla^6 R^4$ term in the low-energy effective action for M-theory. We evaluate explicitly the sums over the discrete exceptional field theory loop momenta that become sums over 1/2-BPS states in the compact exceptional space. These sums can be rewritten as Eisenstein series that solve the homogeneous differential equations that supersymmetry implies for the $\nabla^6 R^4$ coupling. We also show how our results, even though sums over 1/2-BPS states, are consistent with expected 1/4-BPS contributions to the couplings.