Explicit Action of E7(7) on N=8 Supergravity Fields

Abstract

We present an explicit, exact to all orders in gravitational coupling E7(7) symmetry transformations of on-shell N=8 supergravity fields in the gauge with 70 scalars in E7(7)/SU(8) coset space, the local SU(8) symmetry being fixed. The non-linear realization of E7(7) includes a field-dependent SU(8) transformation preserving the unitary gauge. We find the conserved Noether-Gaillard-Zumino current of E7(7) symmetry, the linear part of it being a chiral SU(8) symmetry. We comment on the conformal realization of the E7(7) algebra which includes a dilatation operator. We hope that these results can be useful for studies of anomalies/absence of anomalies and the UV behavior of N=8 supergravity.

25 pages, LaTeX, no figures; v2: typos corrected

References in corpus (16)

• String Theory Dynamics In Various Dimensions
• Unity of Superstring Dualities
• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• Twenty Years of the Weyl Anomaly
• Three-Loop Superfiniteness of N=8 Supergravity
• Is N = 8 Supergravity Ultraviolet Finite?
• E(7) Symmetric Area of the Black Hole Horizon
• Ultraviolet properties of Maximal Supergravity
• Conformal and Quasiconformal Realizations of Exceptional Lie Groups
• Inherited Twistor-Space Structure of Gravity Loop Amplitudes
• On N=8 attractors
• The No-Triangle Hypothesis for N=8 Supergravity
• Decoupling Supergravity from the Superstring
• Twistor Actions for Self-Dual Supergravities
• On the structure of scattering amplitudes in N=4 super Yang-Mills and N=8 supergravity
• The Effective Action of N=8 Supergravity

Cited by in corpus (40)

• What is the Simplest Quantum Field Theory?
• A Duality For The S Matrix
• The Ultraviolet Behavior of N=8 Supergravity at Four Loops
• Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N=8 Supergravity
• The S-Matrix in Twistor Space
• Exacting N=4 Superconformal Symmetry
• The Tree Formula for MHV Graviton Amplitudes
• E7(7) symmetry in perturbatively quantised N=8 supergravity
• E{7(7)} Symmetry and Finiteness of N=8 Supergravity
• R^4 counterterm and E7(7) symmetry in maximal supergravity
• N=8 Counterterms and E7(7) Current Conservation
• Tree-Level Amplitudes in N=8 Supergravity
• The footprint of E7 in amplitudes of N=8 supergravity
• Three Applications of a Bonus Relation for Gravity Amplitudes
• Unraveling L_{n,k}: Grassmannian Kinematics
• E7(7) invariant Lagrangian of d=4 N=8 supergravity
• Invariant Differential Operators for Non-Compact Lie Algebras Parabolically Related to Conformal Lie Algebras
• N=8 Supergravity 4-point Amplitudes
• N=8 Supergravity on the Light Cone
• The Ultraviolet Finiteness of N=8 Supergravity
• New E77 invariants and amplitudes
• Soft theorems in maximally supersymmetric theories
• On Cancellations of Ultraviolet Divergences in Supergravity Amplitudes
• Exceptional Lie Algebras, SU(3) and Jordan Pairs Part 2: Zorn-type Representations
• More on N=8 Attractors
• On a possibility of a UV finite N=8 supergravity
• Supersymmetry constraints on the R^4 multiplet in type IIB on T^2
• Exceptional Lie Algebra $E_{7(-25)}$ (Multiplets and Invariant Differential Operators)
• On the dualization of scalars into (d-2)-forms in supergravity. Momentum maps, R-symmetry and gauged supergravity
• Nonlinear (Super)Symmetries and Amplitudes
• Duality Constraints on Counterterms in $\mathcal{N}=5,6$ Supergravities
• Iwasawa N=8 Attractors
• The Action with Manifest E7 Type Symmetry
• A Note on Single Soft Scalar Emission of $\mathcal{N}=8$ SUGRA and $E_{7(7)}$ Symmetry
• Sextonions, Zorn Matrices, and ${\mathbf{e}}_{7\frac{1}{2}}$
• Light-by-Light Scattering Effect in Light-Cone Supergraphs
• On quantum compatibility of counterterm deformations and duality symmetries in $\mathcal{N}\ge 5$ supergravities
• Infrared Finite Observables in N=8 Supergravity
• Deformation of d=4, N> 4 Supergravities Breaks Nonlinear Local Supersymmetry
• Classification of Invariant Differential Operators for Non-Compact Lie Algebras via Parabolic Relations