On Absence of 3-loop Divergence in N=4 Supergravity

Abstract

We argue that N=4 supergravity is 3-loop UV finite because the relevant supersymmetric candidate counterterm is known to be SL(2, R)x SO(6) invariant, which violates the Noether-Gaillard-Zumino current conservation. Analogous arguments, based on the universality properties of groups of type E7, also apply to N=5,6,8 in 4,5,7 loops, respectively, since the 1/N BPS invariants break duality symmetry between Bianchi identities and quantum corrected vector field equations.

5 pages

References in corpus (9)

• Three-Loop Superfiniteness of N=8 Supergravity
• E7(7) constraints on counterterms in N=8 supergravity
• Absence of Three-Loop Four-Point Divergences in N=4 Supergravity
• Covariant procedures for perturbative non-linear deformation of duality-invariant theories
• N=8 Counterterms and E7(7) Current Conservation
• Degeneration of Groups of Type E7 and Minimal Coupling in Supergravity
• Born-Infeld with Higher Derivatives
• N=2 Supersymmetry and U(1)-Duality
• Creation of Matter in the Universe and Groups of Type E7

Cited by in corpus (10)

• The Ultraviolet Properties of N=4 Supergravity at Four Loops
• One-loop four-point amplitudes in pure and matter-coupled N <= 4 supergravity
• The Ultraviolet Structure of Half-Maximal Supergravity with Matter Multiplets at Two and Three Loops
• Anomalies and divergences in N=4 supergravity
• Covariant actions for models with non-linear twisted self-duality
• One-loop four-graviton amplitudes in N=4 supergravity models
• New E77 invariants and amplitudes
• Conjecture on Hidden Superconformal Symmetry of N=4 Supergravity
• One-loop Amplitudes for N=2 Homogeneous Supergravities
• Arguments Against a Finite N=8 Supergravity