Polylogarithms from the bound state S-matrix

Abstract

Higher-point functions of gauge invariant composite operators in N=4 super Yang-Mills theory can be computed via triangulation. The elementary tile in this process is the hexagon introduced for the evaluation of structure constants. A glueing procedure welding the tiles back together is needed to return to the original object. In this note we present work in progress on n-point functions of BPS operators. In this case, quantum corrections are entirely carried by the glueing procedure. The lowest non-elementary process is the glueing of three adjacent tiles by the exchange of two single magnons. This problem has been analysed before. With a view to resolving some conceptional questions and to generalising to higher processes we are trying to develop an algorithmic approach using the representation of hypergeometric sums as integrals over Euler kernels.

11 pages, 2 figures

References in corpus (11)

• Strings in flat space and pp waves from $\mathcal{N}=4$ Super Yang Mills
• Classical Polylogarithms for Amplitudes and Wilson Loops
• Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
• Motivic Amplitudes and Cluster Coordinates
• Hexagonalization of Correlation Functions
• Structure Constants and Integrable Bootstrap in Planar N=4 SYM Theory
• Tessellating cushions: four-point functions in N=4 SYM
• The Dressing Factor and Crossing Equations
• The Bound State S-Matrix for AdS5 x S5 Superstring
• Hexagonalization of Correlation Functions II: Two-Particle Contributions
• Positivity of hexagon perturbation theory

Cited by in corpus (3)

• The SAGEX Review on Scattering Amplitudes, Chapter 8: Half BPS correlators
• Pentagon OPE resummation in N=4 SYM: hexagons with one effective particle contribution
• Bound State Scattering Simplified