Structure Constants in $\mathcal{N} = 4$ SYM and Separation of Variables

TL;DR

This paper introduces a novel framework for calculating three-point functions in planar $ ext{N}=4$ SYM using Separation of Variables, tested at various orders and sectors, with indications of including wrapping effects.

Contribution

It presents a new integral-based formalism for three-point functions in $ ext{N}=4$ SYM, applicable at weak coupling and capable of incorporating wrapping effects.

Findings

Validated the formalism at leading and next-to-leading orders in the SL(2) sector.

Extended the approach to next-to-next-to-leading orders in the SU(2) sector.

Provided evidence that wrapping effects can be integrated into the framework.

Abstract

We propose a new framework for computing three-point functions in planar $\mathcal{N}=4$ super Yang-Mills where these correlators take the form of multiple integrals of Separation of Variables type. We test this formalism at weak coupling at leading and next-to-leading orders in a non-compact SL(2) sector of the theory and all the way to next-to-next-to-leading orders for a compact SU(2) sector. We find evidence that wrapping effects can also be incorporated.