The vanishing volume of D=4 superspace

Abstract

The volume of on-shell D=4, N=8 superspace is shown to vanish. Despite this, it is shown that there is a fully supersymmetric and duality-invariant candidate d^8 R^4 counterterm corresponding to an anticipated seven-loop logarithmic divergence in D=4. We construct this counterterm explicitly and also give the complete nonlinear extension of the 1/8-BPS d^6 R^4 invariant. Similar results are derived for N=4,5 & 6.

Minor clarifications and references added. Version to be published

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Cited by in corpus (64)

• Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes
• Five-Point Amplitudes in N=4 Super-Yang-Mills Theory and N=8 Supergravity
• Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop
• The Ultraviolet Properties of N=4 Supergravity at Four Loops
• Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops
• Ultraviolet Properties of N = 8 Supergravity at Five Loops
• Absence of Three-Loop Four-Point Divergences in N=4 Supergravity
• Scattering amplitudes in N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity
• The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
• N >= 4 Supergravity Amplitudes from Gauge Theory at Two Loops
• Scattering Amplitudes
• The Ultraviolet Structure of Half-Maximal Supergravity with Matter Multiplets at Two and Three Loops
• Ultraviolet Cancellations in Half-Maximal Supergravity as a Consequence of the Double-Copy Structure
• Equivalent D=3 Supergravity Amplitudes from Double Copies of Three-Algebra and Two-Algebra Gauge Theories
• Two-loop supersymmetric QCD and half-maximal supergravity amplitudes
• The two-loop five-point amplitude in $\mathcal{N}=8$ supergravity
• Double Copy from Homotopy Algebras
• D = 5 maximally supersymmetric Yang-Mills theory diverges at six loops
• Double-Copy Constructions and Unitarity Cuts
• Color-kinematics duality and Sudakov form factor at five loops for N=4 supersymmetric Yang-Mills theory
• Tropical Amplitudes
• The Five-Loop Four-Point Amplitude of N=4 super-Yang-Mills Theory
• Covariant procedures for perturbative non-linear deformation of duality-invariant theories
• Simple encoding of higher derivative gauge and gravity counterterms
• Superconformal symmetry and maximal supergravity in various dimensions
• Gravity as the square of Yang-Mills?
• Four-graviton scattering to three loops in $\mathcal{N}=8$ supergravity
• Anomalies and divergences in N=4 supergravity
• Invariants and divergences in half-maximal supergravity theories
• Minimal unitary representations from supersymmetry
• Covariant actions for models with non-linear twisted self-duality
• An R^4 non-renormalisation theorem in N=4 supergravity
• Cancelling the U(1) Anomaly in the S-matrix of N=4 Supergravity
• The two D6R4 type invariants and their higher order generalisation
• Pure spinor superfields and Born-Infeld theory
• Higher Derivative Supergravities in Diverse Dimensions
• One-loop four-graviton amplitudes in N=4 supergravity models
• Manifesting enhanced cancellations in supergravity: integrands versus integrals
• Soft theorems from anomalous symmetries
• UV cancelations in gravity loop integrands
• Conjecture on Hidden Superconformal Symmetry of N=4 Supergravity
• One-loop Amplitudes for N=2 Homogeneous Supergravities
• Ultraviolet behavior of 6D supersymmetric Yang-Mills theories and harmonic superspace
• Type I/heterotic duality and M-theory amplitudes
• Worldsheet factorization for twistor-strings
• The Color-Dual Fates of $F^3$, $R^3$, and $\mathcal{N}=4$ Supergravity
• Ultraviolet divergences in non-renormalizable supersymmetric theories
• Effective observables for electromagnetic duality from novel amplitude decomposition
• Counterterms in Gravity in the Light-Front Formulation and a D=2 Conformal-like Symmetry in Gravity
• On Absence of 3-loop Divergence in N=4 Supergravity
• Challenges of D=6 N=(1,1) SYM Theory
• Gravity loop integrands from the ultraviolet
• Duality Constraints on Counterterms in $\mathcal{N}=5,6$ Supergravities
• The Action with Manifest E7 Type Symmetry
• Supersymmetry constraints on U-duality invariant deformations of $N\ge 5$ Supergravity
• Superforms in Five-Dimensional, $N=1$ Superspace
• N=2 Supergravity Counterterms, Off and On Shell
• Perturbative higher-derivative terms in N=6 asymmetric orbifolds
• Off-shell invariants of linearized $4D,\mathcal{N}=2$ supergravity in the harmonic approach
• Generalizing the ADM Computation to Quantum Field Theory
• Two-loop n-point anomalous amplitudes in N=4 supergravity
• String Theory, Unification and Quantum Gravity
• Deformation of d=4, N> 4 Supergravities Breaks Nonlinear Local Supersymmetry
• Group-Theoretical Classification of BPS States in D=4 Conformal Supersymmetry: the Case of (1/N)-BPS