5 loops in 24/5 dimensions

Abstract

A first quantised approach to loop amplitudes based on the pure spinor particle is applied to the systematics of four-particle amplitudes in maximally supersymmetric field theories. Counting of fermionic zero modes allows the identification of momentum factors multiplying R**4 in the case of supergravity (and F**4 in the Yang--Mills case) thereby making manifest their ultraviolet properties as a function of dimension, D. For L=2,3,4 loops the leading supergravity divergence is in D=4+6/L dimensions and proportional to d*2L R**4, in line with earlier field theory calculations. However, at five loops there is a radical change in the systematics, suggesting the presence of a contribution with an explicit L=5 logarithmic ultraviolet divergence when D=24/5 that is proportional to d*8 R**4. We further argue that d*8 R**4 should receive contributions from all loops, which would imply that N=8 supergravity (with D=4) is not protected by supersymmetry from a seven-loop divergence.

23 pages, 7 figures. Version published in journal

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Cited by in corpus (64)

• On D=5 super Yang-Mills theory and (2,0) theory
• 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
• Loops in AdS from Conformal Field Theory
• The Ultraviolet Properties of N=4 Supergravity at Four Loops
• Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop
• Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops
• Ultraviolet Properties of N = 8 Supergravity at Five Loops
• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• 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
• On the Singularity Structure of Maximally Supersymmetric Scattering Amplitudes
• The Structure of n-Point One-Loop Open Superstring Amplitudes
• The Ultraviolet Structure of Half-Maximal Supergravity with Matter Multiplets at Two and Three Loops
• The vanishing volume of D=4 superspace
• Nonlocal quantum gravity and M-theory
• Ultraviolet Cancellations in Half-Maximal Supergravity as a Consequence of the Double-Copy Structure
• On duality symmetries of supergravity invariants
• Multi-loop amplitudes in maximally supersymmetric pure spinor field theory
• The two-loop five-point amplitude in $\mathcal{N}=8$ supergravity
• Non-linear gauge transformations in $D=10$ SYM theory and the BCJ duality
• N-Point Tree-Level Scattering Amplitude in the New Berkovits' String
• D = 5 maximally supersymmetric Yang-Mills theory diverges at six loops
• 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
• M-Theory Reconstruction from (2,0) CFT and the Chiral Algebra Conjecture
• Covariant procedures for perturbative non-linear deformation of duality-invariant theories
• Pure spinor superfields -- an overview
• Amplitudes and Ultraviolet Behavior of N=8 Supergravity
• Tree-level amplitudes from the pure spinor superstring
• Four-graviton scattering to three loops in $\mathcal{N}=8$ supergravity
• 10D Super-Yang-Mills Scattering Amplitudes From Its Pure Spinor Action
• Amplitudes at Infinity
• Einstein gravity from the $\mathbb{N}=4$ spinning particle
• Integral invariants in maximally supersymmetric Yang-Mills theories
• Pure spinor superfields and Born-Infeld theory
• The Ultraviolet Finiteness of N=8 Supergravity
• UV cancelations in gravity loop integrands
• Ultraviolet behavior of 6D supersymmetric Yang-Mills theories and harmonic superspace
• Loop amplitudes in maximal supergravity with manifest supersymmetry
• The D^{2k} R^4 Invariants of N=8 Supergravity
• Worldsheet factorization for twistor-strings
• The D^6 R^4 term from three loop maximal supergravity
• Towards the Gravituhedron: New Expressions for NMHV Gravity Amplitudes
• Double Copy from Tensor Products of Metric BV${}^{■}$-algebras
• Spinor frame formalism for amplitudes and constrained superamplitudes of 10D SYM and 11D supergravity
• Divergences and Boundary Modes in N=8 Supergravity
• Tree-Level Color-Kinematics Duality from Pure Spinor Actions
• Counterterms in Gravity in the Light-Front Formulation and a D=2 Conformal-like Symmetry in Gravity
• Gravity loop integrands from the ultraviolet
• The geometry of pure spinor space
• Simplified D=11 Pure Spinor b Ghost
• An off-shell superspace reformulation of D=4, N=4 super-Yang-Mills theory
• Notes on the $D=11$ pure spinor superparticle
• Ultraviolet divergences in maximal supergravity from a pure spinor point of view
• Non-analytic terms of string amplitudes from partial waves
• Pure Spinor Integration from the Collating Formula
• Maximally Supersymmetric Yang-Mills in five dimensions in light-cone superspace
• Constraining non--BPS interactions from counterterms in three loop maximal supergravity
• Higher-dimensional invariants in $6D$ super Yang-Mills theory
• Off- and on-shell harmonic superspaces for 6D SYM theories
• Exceptional symmetries in light-cone superspace