$n$-point correlators of twist-$2$ operators in $SU(N)$ Yang-Mills theory to the lowest perturbative order

TL;DR

This paper calculates the lowest-order perturbative $n$-point correlators of twist-2 operators in $SU(N)$ Yang-Mills theory, providing explicit expressions in both coordinate and momentum space, and constructing their generating functionals.

Contribution

It presents the first explicit computation of $n$-point correlators of twist-2 operators in Yang-Mills theory at lowest perturbative order, including their generating functionals.

Findings

Explicit $n$-point correlators in coordinate and momentum space.

Generating functionals expressed as logarithms of functional determinants.

Results valid in both Minkowskian and Euclidean space.

Abstract

We compute, to the lowest perturbative order in $SU(N)$ Yang-Mills theory, $n$-point correlators in the coordinate and momentum representation of the gauge-invariant twist-$2$ operators with maximal spin along the $p_+$ direction, both in Minkowskian and -- by analytic continuation -- Euclidean space-time. We also construct the corresponding generating functionals. Remarkably, they have the structure of the logarithm of a functional determinant of the identity plus a term involving the effective propagators that act on the appropriate source fields.