N=8 Counterterms and E7(7) Current Conservation

Abstract

We examine conservation of the E7(7) Noether-Gaillard-Zumino current in the presence of N=8 supergravity counterterms using the momentum space helicity formalism, which significantly simplifies the calculations. The main result is that the 4-point counterterms at any loop order L are forbidden by the E7(7) current conservation identity. We also clarify the relation between linearized and full non-linear superinvariants as candidate counterterms. This enables us to show that all n-point counterterms at L=7, 8 are forbidden since they provide a non-linear completions of the 4-point ones. This supports and exemplifies our general proof in arXiv:1103.4115 of perturbative UV finiteness of N=8 supergravity.

18 pages

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Cited by in corpus (36)

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• Scattering Amplitudes
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• Counterterms vs. Dualities
• Covariant procedures for perturbative non-linear deformation of duality-invariant theories
• Superconformal symmetry and maximal supergravity in various dimensions
• Born-Infeld with Higher Derivatives
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• Invariants and divergences in half-maximal supergravity theories
• Covariant actions for models with non-linear twisted self-duality
• Bispinor Auxiliary Fields in Duality-Invariant Electrodynamics Revisited
• N=2 Supersymmetry and U(1)-Duality
• New E77 invariants and amplitudes
• The M5-brane action revisited
• Constitutive relations and Schroedinger's formulation of nonlinear electromagnetic theories
• Twisted Self-Duality for Linearized Gravity in D dimensions
• One-loop Amplitudes for N=2 Homogeneous Supergravities
• Auxiliary superfields in N=1 supersymmetric self-dual electrodynamics
• On duality symmetry in perturbative quantum theory
• Arguments Against a Finite N=8 Supergravity
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• Constitutive relations, off shell duality rotations and the hypergeometric form of Born-Infeld theory
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• Bispinor Auxiliary Fields in Duality-Invariant Electrodynamics Revisited: The U(N) Case
• Supersymmetry constraints on U-duality invariant deformations of $N\ge 5$ Supergravity
• An Update on Perturbative N=8 Supergravity
• New Approach to Duality-Invariant Nonlinear Electrodynamics
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• Enhancement of hidden symmetries and Chern-Simons couplings
• On quantum compatibility of counterterm deformations and duality symmetries in $\mathcal{N}\ge 5$ supergravities
• Deformation of d=4, N> 4 Supergravities Breaks Nonlinear Local Supersymmetry