A tree-level 3-point function in the su(3)-sector of planar N=4 SYM

TL;DR

This paper classifies and computes tree-level 3-point functions involving su(3) operators in planar N=4 SYM, expressing them through Bethe vector scalar products and determinants, and evaluates their semi-classical limit.

Contribution

It provides a classification of 3-point functions with su(3) operators and derives determinant formulas for their structure constants.

Findings

3-point functions expressed via scalar products of Bethe vectors.

Determinant form obtained when second level Bethe roots are trivial.

Semi-classical limit evaluated for large root numbers.

Abstract

We classify the 3-point functions of local gauge-invariant single-trace operators in the scalar sector of planar N=4 supersymmetric Yang-Mills involving at least one su(3) operator. In the case of two su(3) and one su(2) operators, the tree-level 3-point function can be expressed in terms of scalar products of su(3) Bethe vectors. Moreover, if the second level Bethe roots of one of the su(3) operators is trivial (set to infinity), this 3-point function can be written in a determinant form. Using the determinant representation, we evaluate the structure constant in the semi-classical limit, when the number of roots goes to infinity.