Spinning hexagons

Abstract

We reduce the computation of three point function of three spinning operators with arbitrary polarizations in 𝒩 = 4 SYM to a statistical mechanics problem via the hexagon formalism. The central building block of these correlation functions is the hexagon partition function. We explore its analytic structure and use it to generate perturbative data for spinning three point functions. For certain polarizations and any coupling, we express the full asymptotic three point function in determinant form. With the integrability approach established we open the ground to study the large spin limit where dualities with null Wilson loops and integrable pentagons must appear.

Two spinning Konishi operators at three loops.

“…Three-point functions of multiple twist-two spinning operators have been studied recently [13][14][15] via integrability and the OPE, developing novel techniques and uncovering interesting properties. Especially, their large spin limit was bootstrapped exactly and was related to null Wilson loops.…”

Higher-point integrands in $\mathcal{N} = 4$ super Yang-Mills theory

“…For simplicity, we will be working at leading and subleading orders. We are able to extract the two-loop OPE coefficients with two spinning operators and compare with a result that has been previously computed [56][57][58] (see [54] for an integrability-based computation). We will take the Lorentzian OPE limit as explained in the last subsection, and subsequently take the two points to approach each other, x 2 → x 1 , keeping only the first three nontrivial orders.…”

“…Such terms however cannot generate five numerators at two-loop order 31. In principle, we could use integrability data[54,55] for the non-log part of the correlator to fix more coefficients of the ansatz.…”