The Ultraviolet Finiteness of N=8 Supergravity

Abstract

We study counterterms (CT's), candidates for UV divergences in the four-dimensional N=8 supergravity. They have been constructed long ago in a Lorentz covariant on shell superspace and recently in the chiral light-cone (LC) superspace. We prove that all of these CT's are ruled out since they are not available in the real LC superspace. This implies the perturbative UV finiteness of d=4 N=8 supergravity under the assumption that supersymmetry and continuous E7 symmetry are anomaly-free. The proof, based on the chiral nature of CT's in the LC superspace, is a generalization of the perturbative F-term non-renormalization theorem for N=8 supergravity.

18 pages

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Cited by in corpus (19)

• Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes
• E7(7) constraints on counterterms in N=8 supergravity
• Scattering amplitudes in N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity
• Eikonal methods applied to gravitational scattering amplitudes
• E{7(7)} Symmetry and Finiteness of N=8 Supergravity
• Covariant procedures for perturbative non-linear deformation of duality-invariant theories
• N=8 Counterterms and E7(7) Current Conservation
• Amplitudes and Ultraviolet Behavior of N=8 Supergravity
• A Chern-Simons Pandemic
• SUSY Ward identities, Superamplitudes, and Counterterms
• Exceptional Reductions
• Note on Bonus Relations for N=8 Supergravity Tree Amplitudes
• The Action with Manifest E7 Type Symmetry
• On the two-loop divergences in 6D, $\mathcal{N}=(1,1)$ SYM theory
• Quantum Gravity Needs Supersymmetry
• Iwasawa nilpotency degree of non compact symmetric cosets in N-extended Supergravity
• Asymptotic safety and quantum gravity amplitudes
• On two-loop divergences of effective action in $6D$, $\mathcal{N}=(1,1)$ SYM theory
• Deformation of d=4, N> 4 Supergravities Breaks Nonlinear Local Supersymmetry