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Comments on gluon 6-point scattering amplitudes in N=4 SYM at strong coupling

Dumitru Astefanesei, Suguru Dobashi, Katsushi Ito, Horatiu Nastase

TL;DR

The paper investigates gluon scattering at strong coupling in N=4 SYM by applying the Alday–M Maldacena AdS/CFT prescription to six-point (and eight-point) amplitudes. It constructs AdS6-point surfaces via cutting and gluing of the known 4-point solution and analyzes their boundary conditions, revealing extra internal cusps that imply an intermediate virtual momentum line and lead to a mismatch with the field-theory BDS predictions. By extending to eight points and examining collinear limits, the authors highlight where the holographic calculation captures only a subset of diagrams and where cusp-related contributions must be accounted for. The work emphasizes the need for direct gauge-theory tests to determine whether the observed discrepancies signal a limitation of BDS at higher points or reflect missing cusp physics in the AdS construction, and it notes a Regge-like behavior in certain strong-coupling limits.

Abstract

We use the AdS/CFT prescription of Alday and Maldacena \cite{am} to analyze gluon 6-point scattering amplitudes at strong coupling in ${\cal N}=4$ SYM. By cutting and gluing we obtain AdS 6-point amplitudes that contain extra boundary conditions and come close to matching the field theory results. We interpret them as parts of the field theory amplitudes, containing only certain diagrams. We also analyze the collinear limits of 6- and 5-point amplitudes and discuss the results.

Comments on gluon 6-point scattering amplitudes in N=4 SYM at strong coupling

TL;DR

The paper investigates gluon scattering at strong coupling in N=4 SYM by applying the Alday–M Maldacena AdS/CFT prescription to six-point (and eight-point) amplitudes. It constructs AdS6-point surfaces via cutting and gluing of the known 4-point solution and analyzes their boundary conditions, revealing extra internal cusps that imply an intermediate virtual momentum line and lead to a mismatch with the field-theory BDS predictions. By extending to eight points and examining collinear limits, the authors highlight where the holographic calculation captures only a subset of diagrams and where cusp-related contributions must be accounted for. The work emphasizes the need for direct gauge-theory tests to determine whether the observed discrepancies signal a limitation of BDS at higher points or reflect missing cusp physics in the AdS construction, and it notes a Regge-like behavior in certain strong-coupling limits.

Abstract

We use the AdS/CFT prescription of Alday and Maldacena \cite{am} to analyze gluon 6-point scattering amplitudes at strong coupling in SYM. By cutting and gluing we obtain AdS 6-point amplitudes that contain extra boundary conditions and come close to matching the field theory results. We interpret them as parts of the field theory amplitudes, containing only certain diagrams. We also analyze the collinear limits of 6- and 5-point amplitudes and discuss the results.

Paper Structure

This paper contains 13 sections, 121 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Review
  3. Six-point scattering amplitudes
  4. Six-point functions: field theory
  5. Six-point amplitudes: AdS
  6. Mismatch interpretation
  7. Eight point function
  8. Collinear limits
  9. Conclusions
  10. Appendix
  11. Integrals
  12. Subleading terms in the action
  13. Fake cusp calculation

Figures (7)

  • Figure 1: Solution 1: $y_0=1/2(|y_1y_2|+y_1y_2-|y_1|y_2+y_1|y_2|)$
  • Figure 2: Solution 2: $y_0=y_1|y_2|$
  • Figure 3: Configuration after the Lorentz boost in the 04 plane for solution 1, $y_0$$=1/2(|y_1y_2|+y_1y_2-|y_1|y_2+y_1y_2)$ with a=1, b=0.5.
  • Figure 4: Configuration after the Lorentz boost in the 04 plane for solution 2, $y_0=y_1|y_2|$ with a=1, b=0.5.
  • Figure 5: a) Conjectured amplitude calculated by solution 2. b) Conjectured amplitude calculated by solution 1. c) Conjectured amplitude calculated by 8-point function solution.
  • ...and 2 more figures