E{7(7)} Symmetry and Finiteness of N=8 Supergravity

Abstract

We study N=8 supergravity deformed by the presence of the candidate counterterms. We show that even though they are invariant under undeformed E{7(7)}, all of the candidate counterterms violate the deformed E{7(7)} current conservation. The same conclusion follows from the uniqueness of the Lorentz and SU(8) covariant, E{7(7)} invariant unitarity constraint expressing the 56-dimensional E{7(7)} doublet via 28 independent vectors. Therefore E{7(7)} duality predicts the all-loop UV finiteness of perturbative N=8 supergravity.

18 pages

References in corpus (13)

• Three-Loop Superfiniteness of N=8 Supergravity
• Generating Tree Amplitudes in N=4 SYM and N=8 SG
• E7(7) constraints on counterterms in N=8 supergravity
• Stringy KLT relations, global symmetries, and E_7(7) violation
• On duality symmetries of supergravity invariants
• E7(7) symmetry in perturbatively quantised N=8 supergravity
• Counterterms vs. Dualities
• Explicit Action of E7(7) on N=8 Supergravity Fields
• The footprint of E7 in amplitudes of N=8 supergravity
• E_7(7) on the Light Cone
• N=8 Supergravity 4-point Amplitudes
• The Ultraviolet Finiteness of N=8 Supergravity
• The D^{2k} R^4 Invariants of N=8 Supergravity

Cited by in corpus (53)

• Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes
• Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops
• Scattering amplitudes in N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity
• One-loop four-point amplitudes in pure and matter-coupled N <= 4 supergravity
• Ultraviolet Cancellations in Half-Maximal Supergravity as a Consequence of the Double-Copy Structure
• D = 5 maximally supersymmetric Yang-Mills theory diverges at six loops
• Tropical Amplitudes
• The Five-Loop Four-Point Amplitude of N=4 super-Yang-Mills Theory
• Twistor Strings for N=8 Supergravity
• Covariant procedures for perturbative non-linear deformation of duality-invariant theories
• N=8 Counterterms and E7(7) Current Conservation
• Superconformal symmetry and maximal supergravity in various dimensions
• Anomalies and divergences in N=4 supergravity
• Invariants and divergences in half-maximal supergravity theories
• Interactions in Higher-Spin Gravity: a Holographic Perspective
• 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
• Conjecture on Hidden Superconformal Symmetry of N=4 Supergravity
• Constitutive relations and Schroedinger's formulation of nonlinear electromagnetic theories
• Summation of all-loop UV Divergences in Maximally Supersymmetric Gauge Theories
• One-loop Amplitudes for N=2 Homogeneous Supergravities
• Eisenstein series for infinite-dimensional U-duality groups
• Twisted Self-Duality for Linearized Gravity in D dimensions
• Loop amplitudes in maximal supergravity with manifest supersymmetry
• Auxiliary superfields in N=1 supersymmetric self-dual electrodynamics
• Worldsheet factorization for twistor-strings
• On duality symmetry in perturbative quantum theory
• Arguments Against a Finite N=8 Supergravity
• The Structure of UV Divergences in Maximally Supersymmetric Gauge Theories
• Challenges of D=6 N=(1,1) SYM Theory
• Nonlinear (Super)Symmetries and Amplitudes
• Constitutive relations, off shell duality rotations and the hypergeometric form of Born-Infeld theory
• Backreaction of Localised Sources in String Compactifications
• Self-Dual N=2 Born-Infeld Theory Through Auxiliary Superfields
• The Action with Manifest E7 Type Symmetry
• Bispinor Auxiliary Fields in Duality-Invariant Electrodynamics Revisited: The U(N) Case
• Supersymmetry constraints on U-duality invariant deformations of $N\ge 5$ Supergravity
• N=2 Supergravity Counterterms, Off and On Shell
• An Update on Perturbative N=8 Supergravity
• New Approach to Duality-Invariant Nonlinear Electrodynamics
• Obstruction to E_{7(7)} Deformation in N=8 Supergravity
• Notophs of N = 8 supergravity
• On the two-loop divergences in 6D, $\mathcal{N}=(1,1)$ SYM theory
• 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
• On two-loop divergences of effective action in $6D$, $\mathcal{N}=(1,1)$ SYM theory
• Perturbative and Non-Perturbative Aspects of N=8 Supergravity
• Divergences in maximal supersymmetric Yang-Mills theories in diverse dimensions
• High Energy Behaviour in Maximally Supersymmetric Gauge Theories in Various Dimensions
• A Master Action for D=11 Supergravity in the Component Formulation
• Exceptional symmetries in light-cone superspace