Fermionic Correlators from Integrability

TL;DR

This paper derives determinant formulas for three-point functions in planar N=4 SYM's su(1|1) sector using integrability, validating the hexagon approach and connecting to six-vertex models, with results applicable at all loops and strong coupling.

Contribution

It provides the first determinant expression for tree-level structure constants in the su(1|1) sector and validates the hexagon program against data, including at strong coupling.

Findings

Determinant formula for tree-level structure constants.

Validation of the hexagon approach with sign factors.

Explicit evaluation of a six-vertex model partition function.

Abstract

We study three-point functions of single-trace operators in the su(1|1) sector of planar N = 4 SYM borrowing several tools based on Integrability. In the most general configuration of operators in this sector, we have found a determinant expression for the tree-level structure constants. We then compare the predictions of the recently proposed hexagon program against all available data. We have obtained a match once additional sign factors are included when the two hexagon form-factors are assembled together to form the structure constants. In the particular case of one BPS and two non-BPS operators we managed to identify the relevant form-factors with a domain wall partition function of a certain six-vertex model. This partition function can be explicitly evaluated and factorizes at all loops. In addition, we use this result to compute the structure constants and show that at strong coupling in the so-called BMN regime, its leading order contribution has a determinant expression.