Solution to the Ward Identities for Superamplitudes

Abstract

Supersymmetry and R-symmetry Ward identities relate on-shell amplitudes in a supersymmetric field theory. We solve these Ward identities for (Next-to)^K MHV amplitudes of the maximally supersymmetric N=4 and N=8 theories. The resulting superamplitude is written in a new, manifestly supersymmetric and R-invariant form: it is expressed as a sum of very simple SUSY and SU(N)_R-invariant Grassmann polynomials, each multiplied by a "basis amplitude". For (Next-to)^K MHV n-point superamplitudes the number of basis amplitudes is equal to the dimension of the irreducible representation of SU(n-4) corresponding to the rectangular Young diagram with N columns and K rows. The linearly independent amplitudes in this algebraic basis may still be functionally related by permutation of momenta. We show how cyclic and reflection symmetries can be used to obtain a smaller functional basis of color-ordered single-trace amplitudes in N=4 gauge theory. We also analyze the more significant reduction that occurs in N=8 supergravity because gravity amplitudes are not ordered. All results are valid at both tree and loop level.

29 pages, published version

References in corpus (34)

• New Relations for Gauge-Theory Amplitudes
• Gluon scattering amplitudes at strong coupling
• Minimal Basis for Gauge Theory Amplitudes
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• Hexagon Wilson loop = six-gluon MHV amplitude
• A Duality For The S Matrix
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• Dual Superconformal Invariance, Momentum Twistors and Grassmannians
• The Ultraviolet Behavior of N=8 Supergravity at Four Loops
• Three-Loop Superfiniteness of N=8 Supergravity
• A note on dual superconformal symmetry of the N=4 super Yang-Mills S-matrix
• Open & Closed vs. Pure Open String Disk Amplitudes
• The Grassmannian Origin Of Dual Superconformal Invariance
• The hexagon Wilson loop and the BDS ansatz for the six-gluon amplitude
• Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N=8 Supergravity
• Generating Tree Amplitudes in N=4 SYM and N=8 SG
• All tree-level amplitudes in N=4 SYM
• Exacting N=4 Superconformal Symmetry
• The ultra-violet question in maximally supersymmetric field theories
• Proof of the MHV vertex expansion for all tree amplitudes in N=4 SYM theory
• Symmetries and analytic properties of scattering amplitudes in N=4 SYM theory
• Recursion Relations, Generating Functions, and Unitarity Sums in N=4 SYM Theory
• On tree-level higher order gravitational couplings in superstring theory
• Supersymmetry Relations and MHV Amplitudes in Superstring Theory
• A note on the UV behaviour of maximally supersymmetric Yang-Mills theories
• From Twistor String Theory To Recursion Relations
• Tree-Level Amplitudes in N=8 Supergravity
• Dual conformal symmetry of 1-loop NMHV amplitudes in N=4 SYM theory
• One-Loop Amplitudes in N=4 Super Yang-Mills and Anomalous Dual Conformal Symmetry
• Proof of the Dual Conformal Anomaly of One-Loop Amplitudes in N=4 SYM
• On UV Finiteness of the Four Loop N=8 Supergravity
• Gluon Tree Amplitudes in Open Twistor String Theory
• A super MHV vertex expansion for N=4 SYM theory
• Diagrammatic Young Projection Operators for U(n)

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• E7(7) constraints on counterterms in N=8 supergravity
• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• Single-valued harmonic polylogarithms and the multi-Regge limit
• Basics of Generalized Unitarity
• Soft Bootstrap and Supersymmetry
• A simple approach to counterterms in N=8 supergravity
• Stringy KLT relations, global symmetries, and E_7(7) violation
• Scattering amplitudes: the most perfect microscopic structures in the universe
• OPE for all Helicity Amplitudes
• R^4 counterterm and E7(7) symmetry in maximal supergravity
• Massive amplitudes on the Coulomb branch of N=4 SYM
• Recursion relations from soft theorems
• On-shell superamplitudes in N<4 SYM
• Quantum integrability and functional equations
• How tropical are seven- and eight-particle amplitudes?
• Amplitudes and Ultraviolet Behavior of N=8 Supergravity
• Unraveling conformal gravity amplitudes
• The Six-Point NMHV amplitude in Maximally Supersymmetric Yang-Mills Theory
• Yangians, S-matrices and AdS/CFT
• Singularities of eight- and nine-particle amplitudes from cluster algebras and tropical geometry
• Efficient Tree-Amplitudes in N=4: Automatic BCFW Recursion in Mathematica
• Graviton and gluon scattering from first principles
• Complete N-Point Superstring Disk Amplitude II. Amplitude and Hypergeometric Function Structure
• Constructing $\mathcal{N}=4$ Coulomb Branch Superamplitudes
• Exact coefficients for higher dimensional operators with sixteen supersymmetries
• SUSY Ward identities, Superamplitudes, and Counterterms
• From Polygon Wilson Loops to Spin Chains and Back
• The Ultraviolet Finiteness of N=8 Supergravity
• OPE for Super Loops
• Massive On-Shell Supersymmetric Scattering Amplitudes
• The D^{2k} R^4 Invariants of N=8 Supergravity
• Review of AdS/CFT Integrability, Chapter V.1: Scattering Amplitudes - a Brief Introduction
• Hexagon POPE: effective particles and tree level resummation
• A manifestly MHV Lagrangian for N=4 Yang-Mills
• Global Poles of the Two-Loop Six-Point N=4 SYM integrand
• Duality Constraints on Counterterms in $\mathcal{N}=5,6$ Supergravities
• Supersymmetry Constraints and String Theory on K3
• The SAGEX Review on Scattering Amplitudes, Chapter 5: Analytic Bootstraps for Scattering Amplitudes and Beyond
• Complete Equivalence Between Gluon Tree Amplitudes in Twistor String Theory and in Gauge Theory
• Supersymmetric Massive Gravity
• One-loop N = 4 super Yang-Mills scattering amplitudes in d dimensions, relation to open strings and polygonal Wilson loops
• Resummed tree heptagon
• An Algebraic Classification of Exceptional EFTs Part II: Supersymmetry
• On-shell Supersymmetry and higher-spin amplitudes
• Deformation of d=4, N> 4 Supergravities Breaks Nonlinear Local Supersymmetry
• Hidden U(N) Symmetry behind N=1 Superamplitudes
• String Theory from Maximal Supersymmetry