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Five W-boson amplitude = near-null decagon

A. V. Belitsky, L. V. Bork, R. N. Lee, A. I. Onishchenko, V. A. Smirnov

TL;DR

This work analyzes the five-W-boson amplitude on the special Coulomb branch of planar N=4 sYM by dimensional reduction from six dimensions, focusing on the near mass-shell regime where external masses are small relative to kinematic invariants. It computes the amplitude to two loops, demonstrates IR logarithm exponentiation governed by the octagon anomalous dimension, and proposes an all-order structure involving Gamma_oct and cusp-like data; it also establishes a duality to the decagon, the square root of a five-point heavy half-BPS operator correlator, validated in the near-null limit. The results extend the known amplitude/correlator dualities from the conformal branch to the Coulomb branch and provide concise all-order conjectures for the five-point case, opening avenues for three-loop analysis and higher-leg amplitudes in the presence of masses. Overall, the paper demonstrates a coherent framework connecting higher-dimensional origins, loop integrals with dual-conformal properties, and deep dualities to heavy operator correlators in a regime where a simplified Gaussian structure emerges.

Abstract

We study a five-leg scattering amplitude on the special Coulomb branch of planar N=4 super Yang-Mills theory. We reach this point of the moduli space of scalar vacuum expectation values by considering six-dimensional N=(1,1) super Yang-Mills theory and reducing it down to four space-time dimensions with extra-dimensional momenta being nonvanishing. This branch is characterized by massive external W-bosons and massless internal gluons propagating in loops. We analyze the five W-boson amplitude in the kinematics when their masses are much smaller than all Mandelstam-like invariants. This is what we dub the near mass-shell limit. We perform calculations to two-loop order in 't Hooft coupling, making use of recent advances in analytic calculations of required Feynman integrals. Our findings confirm exponentiation of infrared logarithms and enable us to conjecture a concise all-order expression for the amplitude in question. We further analyze its duality to the `square root' of a five-point correlation function of infinitely-heavy half-BPS operators, known as the decagon. By considering the near-null limit for inter-operators distances, we verify that the two objects coincide. This observation corroborates the novel Coulomb amplitudes/heavy correlator duality previously observed for four W-boson amplitudes and Sudakov form factors.

Five W-boson amplitude = near-null decagon

TL;DR

This work analyzes the five-W-boson amplitude on the special Coulomb branch of planar N=4 sYM by dimensional reduction from six dimensions, focusing on the near mass-shell regime where external masses are small relative to kinematic invariants. It computes the amplitude to two loops, demonstrates IR logarithm exponentiation governed by the octagon anomalous dimension, and proposes an all-order structure involving Gamma_oct and cusp-like data; it also establishes a duality to the decagon, the square root of a five-point heavy half-BPS operator correlator, validated in the near-null limit. The results extend the known amplitude/correlator dualities from the conformal branch to the Coulomb branch and provide concise all-order conjectures for the five-point case, opening avenues for three-loop analysis and higher-leg amplitudes in the presence of masses. Overall, the paper demonstrates a coherent framework connecting higher-dimensional origins, loop integrals with dual-conformal properties, and deep dualities to heavy operator correlators in a regime where a simplified Gaussian structure emerges.

Abstract

We study a five-leg scattering amplitude on the special Coulomb branch of planar N=4 super Yang-Mills theory. We reach this point of the moduli space of scalar vacuum expectation values by considering six-dimensional N=(1,1) super Yang-Mills theory and reducing it down to four space-time dimensions with extra-dimensional momenta being nonvanishing. This branch is characterized by massive external W-bosons and massless internal gluons propagating in loops. We analyze the five W-boson amplitude in the kinematics when their masses are much smaller than all Mandelstam-like invariants. This is what we dub the near mass-shell limit. We perform calculations to two-loop order in 't Hooft coupling, making use of recent advances in analytic calculations of required Feynman integrals. Our findings confirm exponentiation of infrared logarithms and enable us to conjecture a concise all-order expression for the amplitude in question. We further analyze its duality to the `square root' of a five-point correlation function of infinitely-heavy half-BPS operators, known as the decagon. By considering the near-null limit for inter-operators distances, we verify that the two objects coincide. This observation corroborates the novel Coulomb amplitudes/heavy correlator duality previously observed for four W-boson amplitudes and Sudakov form factors.
Paper Structure (14 sections, 81 equations, 1 figure)

This paper contains 14 sections, 81 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Coulomb branch from generalized dimensional reduction
  3. Trees
  4. Loops and dimensional uplift
  5. Generalized dimensional reduction
  6. Iterative structure of conformal branch amplitudes
  7. Special Coulomb branch amplitudes
  8. Four W-bosons
  9. Five W-bosons
  10. Duality to heavy correlation functions
  11. Octagon
  12. Decagon
  13. Conclusions
  14. Pentabox and other two-loop integrals

Figures (1)

  • Figure 1: World-sheet representation of correlation functions of four- (left) and five-point correlation functions.