# Structure constants at wrapping order

## TL;DR

This paper develops a renormalization method within the hexagon framework to compute structure constants at wrapping order in planar $
abla$=4 SYM, validated against weak and strong coupling results.

## Contribution

It introduces a renormalization procedure for divergences in the hexagon approach, enabling leading wrapping order predictions for structure constants.

## Key findings

- Agreement with four-loop planar correction at weak coupling
- Consistency with string theory results at strong coupling
- Renormalization method resolves divergences in the hexagon framework

## Abstract

We consider structure constants of single trace operators in planar $\mathcal{N}$ = 4 Super-Yang-Mills theory within the hexagon framework. The standard procedure for forming a three point function out of two hexagons develops divergences when the effects of virtual particles wrapping around the operators are taken into account. In this paper, we explain how to renormalize these divergences away and obtain definite predictions, at the leading wrapping order, for some of the structure constants that parameterize the OPE of two chiral primaries. We test our method at weak coupling against the four loop planar correction to the BPS-BPS-Konishi OPE coefficient, derived recently in the field theory. At strong coupling, we compare our expressions with the structure constants obtained in string theory for three semiclassical strings.