Multi-particle finite-volume effects for hexagon tessellations

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.

Ten dimensional symmetry of N=4 SYM correlators

“…see for instance[43,44] for resummations at strong coupling in the context of three-point functions and see[45][46][47] for examples on more generic hexagon form factors in the context of four-and five-point functions at weak coupling.…”

About Calculation of Massless and Massive Feynman Integrals

“…We can calculate Φ 2 (0, n) directly in the way similar to the evaluation of Φ 1 (0, n). The direct calculation is a full agreement of such calculations with (102).…”

Three-point Functions in $\mathcal{N}=4$ SYM at Finite $N_c$ and Background Independence

“…The integrability approach tells us how single-trace correlation functions depend on the 't Hooft coupling λ = N c g 2 YM . However, only the non-extremal correlation functions have been studied, because the non-extremality is related to the so-called bridge length (the number of Wick contractions between a pair of operators), which suppresses the complicated wrapping corrections to the asymptotic formula [13][14][15][16][17].…”