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Multi-Regge Limit of the n-Gluon Bubble Ansatz

J. Bartels, V. Schomerus, M. Sprenger

TL;DR

We address the strong-coupling regime of $n$-gluon scattering in ${\cal N}=4$ SYM by reformulating the amplitude in terms of the Y-system/TBA for AdS$_5$ minimal surfaces ending on an $n$-gon. The main result identifies the multi-Regge limit with the large-volume (large-mass) limit of the auxiliary 1D integrable system, and shows that wall-crossing occurs for $n>6$, introducing residue terms that can be absorbed into a Bethe-ansatz description of the amplitudes. This yields a concrete, algebraic framework (Bethe equations) to capture the leading Regge behavior and the analytic structure of the remainder function $R^{(n)}$ at strong coupling. The findings bridge the 4D Regge limit with 1D quantum integrable systems, offering a path to constrain and potentially interpolate $R^{(n)}$ across coupling regimes via Regge data and polygon Wilson loop OPE insights.

Abstract

We investigate n-gluon scattering amplitudes in the multi-Regge region of N=4 supersymmetric Yang-Mills theory at strong coupling. Through a careful analysis of the thermodynamic bubble ansatz (TBA) for surfaces in AdS5 with n-g(lu)on boundary conditions we demonstrate that the multi-Regge limit probes the large volume regime of the TBA. In reaching the multi-Regge regime we encounter wall-crossing in the TBA for all n>6. Our results imply that there exists an auxiliary system of algebraic Bethe ansatz equations which encode valuable information on the analytical structure of amplitudes at strong coupling.

Multi-Regge Limit of the n-Gluon Bubble Ansatz

TL;DR

We address the strong-coupling regime of -gluon scattering in SYM by reformulating the amplitude in terms of the Y-system/TBA for AdS minimal surfaces ending on an -gon. The main result identifies the multi-Regge limit with the large-volume (large-mass) limit of the auxiliary 1D integrable system, and shows that wall-crossing occurs for , introducing residue terms that can be absorbed into a Bethe-ansatz description of the amplitudes. This yields a concrete, algebraic framework (Bethe equations) to capture the leading Regge behavior and the analytic structure of the remainder function at strong coupling. The findings bridge the 4D Regge limit with 1D quantum integrable systems, offering a path to constrain and potentially interpolate across coupling regimes via Regge data and polygon Wilson loop OPE insights.

Abstract

We investigate n-gluon scattering amplitudes in the multi-Regge region of N=4 supersymmetric Yang-Mills theory at strong coupling. Through a careful analysis of the thermodynamic bubble ansatz (TBA) for surfaces in AdS5 with n-g(lu)on boundary conditions we demonstrate that the multi-Regge limit probes the large volume regime of the TBA. In reaching the multi-Regge regime we encounter wall-crossing in the TBA for all n>6. Our results imply that there exists an auxiliary system of algebraic Bethe ansatz equations which encode valuable information on the analytical structure of amplitudes at strong coupling.

Paper Structure

This paper contains 22 sections, 104 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Multi-Regge kinematics
  3. Kinematic variables
  4. Scattering in the center-of-mass system
  5. Cross ratios in the multi-Regge limit
  6. The n-gluon thermodynamic bubble ansatz
  7. Amplitudes and the Y-system
  8. Y-system and cross ratios
  9. Multi-Regge limit of the TBA for $n \leq 7$ gluons
  10. Review of the hexagon $n=6$
  11. Multi-Regge limit for $n=7$ gluons
  12. Finding the correct limit
  13. Multi-Regge limit of the TBA - general case
  14. Large phase residues and multi-Regge limit
  15. Multi-Regge limit for $n=8$ gluons
  16. ...and 7 more sections

Figures (5)

  • Figure 1: Kinematics of the scattering process $2 \to n-2$. On the right-hand side we show a graphical representation of the dual variables $x_i$.
  • Figure 2: Graphical representation for the cross ratios of the 7-point amplitude.
  • Figure 3: Residue structure for Y-functions in 8-point case.
  • Figure 4: Residue structure for n points. Y-functions not shown in the figure correspond to gray boxes.
  • Figure 5: Residue structure of $\mathit{Y}_{a,1}^{\left[-4\right]}$. For simplicity, the residue dependencies of the other Y-functions are not shown.