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\( {\mathcal{R}^4} \) counterterm and E7(7) symmetry in maximal supergravity

  • Johannes BrödelEmail author
  • Lance J. Dixon
Open Access
Article

Abstract

The coefficient of a potential \( {\mathcal{R}^4} \) counterterm in \( \mathcal{N} = 8 \) supergravity has been shown previously to vanish in an explicit three-loop calculation. The \( {\mathcal{R}^4} \) term respects \( \mathcal{N} = 8 \) supersymmetry; hence this result poses the question of whether another symmetry could be responsible for the cancellation of the three-loop divergence. In this article we investigate possible restrictions from the continuous coset symmetry E 7(7)/SU(8), exploring the limits as a single scalar becomes soft, as well as a double-soft scalar limit relation derived recently by Arkani-Hamed et al. We implement these relations for the matrix elements of the \( {\mathcal{R}^4} \) term that occurs in the low-energy expansion of closed-string treelevel amplitudes. We find that the matrix elements of \( {\mathcal{R}^4} \) that we investigated all obey the double-soft scalar limit relation, including certain non-maximally-helicity-violating sixpoint amplitudes. However, the single-soft limit does not vanish for this latter set of amplitudes, which suggests that the E 7(7) symmetry is broken by the \( {\mathcal{R}^4} \) term.

Keywords

Extended Supersymmetry Supergravity Models 

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Authors and Affiliations

  1. 1.Max Planck Institute for Gravitational Physics (Albert Einstein Institute)GolmGermany
  2. 2.Institute for Theoretical PhysicsLeibniz University HannoverHannoverGermany
  3. 3.SLAC National Accelerator LaboratoryStanford UniversityMenlo ParkU.S.A.

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