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Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory

J. M. Drummond, J. Henn, G. P. Korchemsky, E. Sokatchev

TL;DR

Drummond, Henn, Korchemsky, and Sokatchev demonstrate a dual superconformal symmetry for planar N=4 SYM amplitudes by embedding them in dual superspace. They show manifest dual superconformal covariance for tree-level MHV and NMHV amplitudes, construct compact NMHV tree-level and one-loop NMHV formulas via three-point invariants, and derive anomalous Ward identities governing loop corrections. Infrared divergences break dual conformal invariance, but the finite ratio functions between non-MHV and MHV amplitudes remain dual conformal invariant, a property illustrated explicitly for six points. The framework unifies on-shell superspace, dual superspace, and dual superconformal generators, and points toward connections with Wilson-loop duality and possible twistor-space interpretations, suggesting broad applicability across all N^kMHV amplitudes and couplings.

Abstract

We argue that the scattering amplitudes in the maximally supersymmetric N=4 super-Yang-Mills theory possess a new symmetry which extends the previously discovered dual conformal symmetry. To reveal this property we formulate the scattering amplitudes as functions in the appropriate dual superspace. Rewritten in this form, all tree-level MHV and next-to-MHV amplitudes exhibit manifest dual superconformal symmetry. We propose a new, compact and Lorentz covariant formula for the tree-level NMHV amplitudes for arbitrary numbers and types of external particles. The dual conformal symmetry is broken at loop level by infrared divergences. However, we provide evidence that the anomalous contribution to the MHV and NMHV superamplitudes is the same and, therefore, their ratio is a dual conformal invariant function. We identify this function by an explicit calculation of the six-particle amplitudes at one loop. We conjecture that these properties hold for all, MHV and non-MHV, superamplitudes in N=4 SYM both at weak and at strong coupling.

Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory

TL;DR

Drummond, Henn, Korchemsky, and Sokatchev demonstrate a dual superconformal symmetry for planar N=4 SYM amplitudes by embedding them in dual superspace. They show manifest dual superconformal covariance for tree-level MHV and NMHV amplitudes, construct compact NMHV tree-level and one-loop NMHV formulas via three-point invariants, and derive anomalous Ward identities governing loop corrections. Infrared divergences break dual conformal invariance, but the finite ratio functions between non-MHV and MHV amplitudes remain dual conformal invariant, a property illustrated explicitly for six points. The framework unifies on-shell superspace, dual superspace, and dual superconformal generators, and points toward connections with Wilson-loop duality and possible twistor-space interpretations, suggesting broad applicability across all N^kMHV amplitudes and couplings.

Abstract

We argue that the scattering amplitudes in the maximally supersymmetric N=4 super-Yang-Mills theory possess a new symmetry which extends the previously discovered dual conformal symmetry. To reveal this property we formulate the scattering amplitudes as functions in the appropriate dual superspace. Rewritten in this form, all tree-level MHV and next-to-MHV amplitudes exhibit manifest dual superconformal symmetry. We propose a new, compact and Lorentz covariant formula for the tree-level NMHV amplitudes for arbitrary numbers and types of external particles. The dual conformal symmetry is broken at loop level by infrared divergences. However, we provide evidence that the anomalous contribution to the MHV and NMHV superamplitudes is the same and, therefore, their ratio is a dual conformal invariant function. We identify this function by an explicit calculation of the six-particle amplitudes at one loop. We conjecture that these properties hold for all, MHV and non-MHV, superamplitudes in N=4 SYM both at weak and at strong coupling.

Paper Structure

This paper contains 39 sections, 227 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Dual conformal symmetry of gluon amplitudes
  3. MHV gluon tree-level amplitudes
  4. On-shell space and full space
  5. Dual space
  6. Dual conformal symmetry
  7. Dual conformal transformation properties of the MHV tree-level gluon amplitudes
  8. Split-helicity gluon amplitudes at tree level
  9. Dual conformal boost generators in the full space
  10. Dual conformal properties of the complete MHV amplitude
  11. ${\cal N}=4$ supersymmetry and scattering amplitudes
  12. ${\cal N}=4$ gluon supermultiplet
  13. Covariant on-shell ${\cal N}=4$ superspace
  14. Superamplitudes in ${\cal N}=4$ SYM
  15. Dual superconformal symmetry of the ${\cal N}=4$ superamplitudes
  16. ...and 24 more sections

Figures (1)

  • Figure 1: Diagrammatic representation of the scattering amplitude/Wilson loop duality. The dashed line depicts the contour $C_n$.