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The super-correlator/super-amplitude duality: Part I

Burkhard Eden, Paul Heslop, Gregory P. Korchemsky, Emery Sokatchev

TL;DR

This work proposes and tests a supersymmetric extension of the amplitude/correlation duality in planar N=4 SYM by promoting bosonic correlators to analytic super-correlators of the N=4 stress-tensor multiplet. In the light-cone limit, these super-correlators reproduce the square of the corresponding super-amplitudes, with loop corrections generated via Lagrangian insertions and organized through the analytic/harmonic superspace formalism. The NMHV tree case is explicitly demonstrated, showing exact matching of residues with R-invariants and momentum-twistor structures, supporting a broader all-loop picture where correlators encode amplitude integrands. The framework highlights a rich interplay between chiral Grassmann analyticity, harmonic variables, and dual superconformal symmetry, suggesting a deep, finite, four-dimensional description of amplitudes through stress-tensor multiplet correlators and guiding future explorations beyond the chiral sector and toward a possible Wilson-loop dual picture.

Abstract

We extend the recently discovered duality between MHV amplitudes and the light-cone limit of correlation functions of a particular type of local scalar operators to generic non-MHV amplitudes in planar N=4 SYM theory. We consider the natural generalization of the bosonic correlators to super-correlators of stress-tensor multiplets and show, in a number of examples, that their light-cone limit exactly reproduces the square of the matching super-amplitudes. Our correlators are computed at Born level. If all of their points form a light-like polygon, the correlator is dual to the tree-level amplitude. If a subset of points are not on the polygon but are integrated over, they become Lagrangian insertions generating the loop corrections to the correlator. In this case the duality with amplitudes holds at the level of the integrand. We build up the superspace formalism needed to formulate the duality and present the explicit example of the n-point NMHV tree amplitude as the dual of the lowest nilpotent level in the correlator.

The super-correlator/super-amplitude duality: Part I

TL;DR

This work proposes and tests a supersymmetric extension of the amplitude/correlation duality in planar N=4 SYM by promoting bosonic correlators to analytic super-correlators of the N=4 stress-tensor multiplet. In the light-cone limit, these super-correlators reproduce the square of the corresponding super-amplitudes, with loop corrections generated via Lagrangian insertions and organized through the analytic/harmonic superspace formalism. The NMHV tree case is explicitly demonstrated, showing exact matching of residues with R-invariants and momentum-twistor structures, supporting a broader all-loop picture where correlators encode amplitude integrands. The framework highlights a rich interplay between chiral Grassmann analyticity, harmonic variables, and dual superconformal symmetry, suggesting a deep, finite, four-dimensional description of amplitudes through stress-tensor multiplet correlators and guiding future explorations beyond the chiral sector and toward a possible Wilson-loop dual picture.

Abstract

We extend the recently discovered duality between MHV amplitudes and the light-cone limit of correlation functions of a particular type of local scalar operators to generic non-MHV amplitudes in planar N=4 SYM theory. We consider the natural generalization of the bosonic correlators to super-correlators of stress-tensor multiplets and show, in a number of examples, that their light-cone limit exactly reproduces the square of the matching super-amplitudes. Our correlators are computed at Born level. If all of their points form a light-like polygon, the correlator is dual to the tree-level amplitude. If a subset of points are not on the polygon but are integrated over, they become Lagrangian insertions generating the loop corrections to the correlator. In this case the duality with amplitudes holds at the level of the integrand. We build up the superspace formalism needed to formulate the duality and present the explicit example of the n-point NMHV tree amplitude as the dual of the lowest nilpotent level in the correlator.

Paper Structure

This paper contains 35 sections, 172 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The bosonic correlators/MHV amplitudes duality
  3. New proposal: Super-correlators/super-amplitudes duality
  4. The correlators/scattering amplitudes duality
  5. Scattering super-amplitudes
  6. The bosonic correlators/MHV amplitudes duality
  7. New proposal: the super-correlators/super-amplitudes duality
  8. Chirality vs Grassmann analyticity
  9. Formulation of the new duality
  10. Iterative structure of the Lagrangian insertions
  11. The ${\cal N}=4$ stress-tensor multiplet in analytic superspace
  12. The ${\cal N}=4$ chiral vector multiplet as a 1/2 BPS multiplet
  13. ${\cal N}=4$ harmonic variables
  14. The ${\cal N}=4$ chiral vector multiplet as an analytic superfield
  15. The ${\cal N}=4$ stress-tensor multiplet as an analytic superfield
  16. ...and 20 more sections

Figures (1)

  • Figure 1: Feynman diagrams providing the dominant contribution to the correlator $\frac{1}{3} (\theta_t^+)^4\langle{ {\cal L}(x_t) \prod_{i\neq t} {\cal O}(x_i) }\rangle$ in the double scaling limit, $x_{st}^2\to 0$ and $x_{i,i+1}^2\to 0$, to lowest order in the coupling. Solid and cirly lines denote scalar and gauge field propagators, respectively.