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Cancellation of divergences up to three loops in exceptional field theory

  • Guillaume Bossard
  • Axel KleinschmidtEmail author
Open Access
Regular Article - Theoretical Physics

Abstract

We consider the tetrahedral three-loop diagram in Ed exceptional field theory evaluated as a scalar diagram for four external gravitons. At lowest order in momenta, this diagram contributes to the ∇6R4 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 ∇6R4 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.

Keywords

Extended Supersymmetry Gauge Symmetry M-Theory Supergravity Models 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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© The Author(s) 2018

Authors and Affiliations

  1. 1.Centre de Physique Théorique, Ecole Polytechnique, CNRS, Université Paris-SaclayPalaiseau cedexFrance
  2. 2.Dipartimento di FisicaUniversità di Roma Tor VergataRomeItaly
  3. 3.Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut)PotsdamGermany
  4. 4.International Solvay InstitutesBrusselsBelgium

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