On UV Finiteness of the Four Loop N=8 Supergravity

Abstract

The 4-loop 4-point amplitude in N=8 d=4 supergravity is UV finite due to supersymmetry. Even better UV behavior of the 4-loop 4-point amplitude, analogous to that of N=4 SYM theory, has been recently established by computation in [1]. All n-point 4-loop amplitudes with n greater than 5 are finite on dimensional grounds. However, the situation with the 5-point amplitudes remained unclear. In this paper we will show that the 5-point 4-loop amplitude must be finite due to supersymmetry, despite the fact that $R^5$ has a supersymmetric generalization for N=1, N=2 and N=4 SUSY. This means that all 4-loop amplitudes in N = 8 supergravity are UV finite. We also discuss the current expectations for higher loops.

8 p

References in corpus (12)

• The Ultraviolet Behavior of N=8 Supergravity at Four Loops
• Three-Loop Superfiniteness of N=8 Supergravity
• Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N=8 Supergravity
• Ultraviolet properties of Maximal Supergravity
• Non-renormalisation Conditions in Type II String Theory and Maximal Supergravity
• New Higher-Derivative $R^4$ Theorems
• Integral invariants in N=4 SYM and the effective action for coincident D-branes
• The ultra-violet question in maximally supersymmetric field theories
• Decoupling Supergravity from the Superstring
• The One-Loop Five-Graviton Amplitude and the Effective Action
• E_7(7) on the Light Cone
• Eleven-Dimensional Supergravity in Light-Cone Superspace

Cited by in corpus (20)

• Stringy KLT relations, global symmetries, and E_7(7) violation
• A simple approach to counterterms in N=8 supergravity
• The Tree Formula for MHV Graviton Amplitudes
• Multiparticle one-loop amplitudes and S-duality in closed superstring theory
• Solution to the Ward Identities for Superamplitudes
• R^4 counterterm and E7(7) symmetry in maximal supergravity
• Amplitudes and Ultraviolet Behavior of N=8 Supergravity
• Towards Loop Quantum Supergravity (LQSG)
• Perturbative and Non-perturbative N =8 Supergravity
• Spectrum Generating Conformal and Quasiconformal U-Duality Groups, Supergravity and Spherical Vectors
• Reduction of Couplings and its application in Particle Physics
• SUSY Ward identities, Superamplitudes, and Counterterms
• Observations on Arithmetic Invariants and U-Duality Orbits in N =8 Supergravity
• Perfecting one-loop BCJ numerators in SYM and supergravity
• Finite Unified Theories and the Higgs boson
• Exceptional Reductions
• The LHC Higgs Boson Discovery: Implications for Finite Unified Theories
• Minimal unitary representation of SO*(8) = SO(6,2) and its SU(2) deformations as massless 6D conformal fields and their supersymmetric extensions
• Iwasawa N=8 Attractors
• Finite Theories Before and After the Discovery of a Higgs Boson at the LHC