Multi-particle finite-volume effects for hexagon tessellations

TL;DR

This paper investigates finite-volume effects in hexagon tessellations for five-point functions in N=4 super Yang-Mills, simplifying calculations of mirror magnon contributions and exploring braiding prescriptions.

Contribution

It introduces a simplified method for computing two-magnon mirror contributions in hexagon tessellations, enhancing the understanding of finite-volume effects in integrability-based correlation functions.

Findings

Mirror-particle contributions yield hyperlogarithms of weight two.

Simplified summation techniques improve calculation efficiency.

Results inform braiding prescription analysis.

Abstract

Correlation functions of gauge-invariant composite operators in N=4 super Yang-Mills theory can be computed by integrability using triangulations. The elementary tile in this process is the hexagon, which should be glued by appropriately inserting resolutions of the identity involving virtual ("mirror") magnons. We consider this problem for five-point functions of protected operators. At one-loop in the 't Hooft coupling, it is necessary to glue three adjacent tiles which involves two virtual magnons scattering among each other. We show that the result can be simplified by using an adapted mirror rotation and employing appropriate summation techniques. The mirror-particle contributions then yield hyperlogarithms of weight two. Finally, we use these results to investigate braiding prescriptions introduced in earlier work on the problem.