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Mandelstam cuts and light-like Wilson loops in N=4 SUSY

L. N. Lipatov, A. Prygarin

TL;DR

The paper analytically continues the two-loop six-point remainder function in N=4 SYM, derived from a light-like Wilson loop (GSVV), into the multi-Regge kinematics to test its consistency with BFKL predictions. The leading logarithmic term reproduces the Mandelstam-cut contribution found in the BFKL framework, while subleading terms emerge as pure imaginary and were not previously obtained via unitarity methods, reinforcing the Wilson-loop/planar-MHV duality. The results demonstrate that the Wilson-loop approach correctly captures essential high-energy analytic structure and provide new information about beyond-LLA contributions. This work strengthens the link between Wilson-loop calculations and scattering amplitudes in N=4 SYM at weak coupling and paves the way for a more complete understanding of Mandelstam cuts in this context.

Abstract

We perform an analytic continuation of the two-loop remainder function for the six-point planar MHV amplitude in N=4 SUSY, found by Goncharov, Spradlin, Vergu and Volovich from the light-like Wilson loop representation. The remainder function is continued into a physical region, where all but two energy invariants are negative. It turns out to be pure imaginary in the multi-Regge kinematics, which is in an agreement with the predictions based on the Steinmann relations for the Regge poles and Mandelstam cut contributions. The leading term reproduces correctly the expression calculated by one of the authors in the BFKL approach, while the subleading term presents a result, that was not yet found with the use of the unitarity techniques. This supports the applicability of the Wilson loop approach to the planar MHV amplitudes in N=4 SUSY.

Mandelstam cuts and light-like Wilson loops in N=4 SUSY

TL;DR

The paper analytically continues the two-loop six-point remainder function in N=4 SYM, derived from a light-like Wilson loop (GSVV), into the multi-Regge kinematics to test its consistency with BFKL predictions. The leading logarithmic term reproduces the Mandelstam-cut contribution found in the BFKL framework, while subleading terms emerge as pure imaginary and were not previously obtained via unitarity methods, reinforcing the Wilson-loop/planar-MHV duality. The results demonstrate that the Wilson-loop approach correctly captures essential high-energy analytic structure and provide new information about beyond-LLA contributions. This work strengthens the link between Wilson-loop calculations and scattering amplitudes in N=4 SYM at weak coupling and paves the way for a more complete understanding of Mandelstam cuts in this context.

Abstract

We perform an analytic continuation of the two-loop remainder function for the six-point planar MHV amplitude in N=4 SUSY, found by Goncharov, Spradlin, Vergu and Volovich from the light-like Wilson loop representation. The remainder function is continued into a physical region, where all but two energy invariants are negative. It turns out to be pure imaginary in the multi-Regge kinematics, which is in an agreement with the predictions based on the Steinmann relations for the Regge poles and Mandelstam cut contributions. The leading term reproduces correctly the expression calculated by one of the authors in the BFKL approach, while the subleading term presents a result, that was not yet found with the use of the unitarity techniques. This supports the applicability of the Wilson loop approach to the planar MHV amplitudes in N=4 SUSY.

Paper Structure

This paper contains 6 sections, 28 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Analytic continuation of GSVV formula
  3. BFKL approach and BDS amplitudes
  4. Analytic continuation -discussions
  5. Conclusion
  6. Acknowledgments

Figures (4)

  • Figure 1: The BDS violating part appears in the region $s,s_2>0;\,s_1,s_3<0$.
  • Figure 2: The dual coordinates of the transverse momenta.
  • Figure 3: The "unitarity" triangle.
  • Figure 4: The region of the reduced cross ratios where the analytic continuation is performed.