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arXiv · 1712.02793

Cancellation of divergences up to three loops in exceptional field theory

Guillaume Bossard·Axel Kleinschmidt
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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.

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Guillaume Bossard, Axel Kleinschmidt. 2017-12-07. Cancellation of divergences up to three loops in exceptional field theory. https://doi.org/10.1007/jhep03(2018)100

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