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

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

TL;DR

<3-5 sentence high-level summary> The paper extends the duality between stress-tensor multiplet correlators and scattering super-amplitudes in planar ${\cal N}=4$ SYM to a broad set of non-MHV amplitudes, using light-like limits and Lagrangian insertions to relate tree-level correlators to NMHV and NNMHV amplitudes. It provides a sequence of nontrivial checks at five- and six-point kinematics, including exact parity-odd agreements in the six-point one-loop NMHV sector, and develops an explicit x-space toolkit to translate correlators into amplitude integrands, including the use of pentagon/box bases and harmonic analyticity. The results support the conjecture that integrands of all ${\rm N^kMHV}$ amplitudes at any loop can be described by correlators of stress-tensor multiplets, aligning with BCFW/momentum-twistor constructions and suggesting a unified generating object for the full integrand structure. The work also demonstrates practical methods for reconstructing full correlators from lower-point data and provides concrete checks against independent amplitude-formalisms, with potential implications for simplifying higher-point, higher-loop computations.

Abstract

We continue the study of the duality between super-correlators and scattering super-amplitudes in planar N=4 SYM. We provide a number of further examples supporting the conjectured duality relation between these two seemingly different objects. We consider the five- and six-point one-loop NMHV and the six-point tree-level NNMHV amplitudes, obtaining them from the appropriate correlators of strength tensor multiplets in N=4 SYM. In particular, we find exact agreement between the rather non-trivial parity-odd sector of the integrand of the six-point one-loop NMHV amplitude, as obtained from the correlator or from BCFW recursion relations. Together these results lead to the conjecture that the integrands of any N^kMHV amplitude at any loop order in planar N=4 SYM can be described by the correlators of stress-tensor multiplets.

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

TL;DR

<3-5 sentence high-level summary> The paper extends the duality between stress-tensor multiplet correlators and scattering super-amplitudes in planar SYM to a broad set of non-MHV amplitudes, using light-like limits and Lagrangian insertions to relate tree-level correlators to NMHV and NNMHV amplitudes. It provides a sequence of nontrivial checks at five- and six-point kinematics, including exact parity-odd agreements in the six-point one-loop NMHV sector, and develops an explicit x-space toolkit to translate correlators into amplitude integrands, including the use of pentagon/box bases and harmonic analyticity. The results support the conjecture that integrands of all amplitudes at any loop can be described by correlators of stress-tensor multiplets, aligning with BCFW/momentum-twistor constructions and suggesting a unified generating object for the full integrand structure. The work also demonstrates practical methods for reconstructing full correlators from lower-point data and provides concrete checks against independent amplitude-formalisms, with potential implications for simplifying higher-point, higher-loop computations.

Abstract

We continue the study of the duality between super-correlators and scattering super-amplitudes in planar N=4 SYM. We provide a number of further examples supporting the conjectured duality relation between these two seemingly different objects. We consider the five- and six-point one-loop NMHV and the six-point tree-level NNMHV amplitudes, obtaining them from the appropriate correlators of strength tensor multiplets in N=4 SYM. In particular, we find exact agreement between the rather non-trivial parity-odd sector of the integrand of the six-point one-loop NMHV amplitude, as obtained from the correlator or from BCFW recursion relations. Together these results lead to the conjecture that the integrands of any N^kMHV amplitude at any loop order in planar N=4 SYM can be described by the correlators of stress-tensor multiplets.

Paper Structure

This paper contains 25 sections, 172 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The duality
  3. Five-point one-loop NMHV and six-point tree NNMHV
  4. Loop corrections to the four-point correlator $G_{4;0}$
  5. The $G_{4;0}$ $\leftrightarrow$ MHV$_4$ duality
  6. The $G_{5;1}^{(0)}$ $\leftrightarrow$ NMHV$_5^{(0)}$ duality
  7. The $G^{(1)}_{5;1}$ $\leftrightarrow$ NMHV$_5^{(1)}$ duality
  8. The $G_{6;2}^{(0)}$ $\leftrightarrow$ NNMHV$_6^{(0)}$ duality
  9. The hexagon limit of the correlator $G^{(0)}_{6;2}$
  10. Evaluating ${\widehat{{\cal A}}}_{n;{\overline{\rm MHV}}}^{\rm tree}$
  11. Evaluating $(\widehat{{\cal A}}^{\text{tree}}_{6;\mathrm{NMHV} })^2$
  12. The six-point one-loop NMHV amplitude
  13. An $x$-space toolkit for 6-point one-loop amplitudes
  14. MHV$_6^{(1)}$ revisited
  15. NMHV$_6^{(0)}$
  16. ...and 10 more sections

Figures (1)

  • Figure 1: The different light-cone limits taken for the points of the correlators $\langle{{\cal O}{\cal O}{\cal O}{\cal O}{\cal L}}\rangle$ and $\langle{{\cal O}{\cal O}{\cal O}{\cal O}{\cal L}{\cal L}}\rangle$. Operators at neighbouring vertices of a polygon are light-like separated, whereas those inside the polygon are located at arbitrary points.