Higher-spin correlators

TL;DR

This paper predicts the all-loop structure constant for a three-point correlator involving higher spin operators in N=4 super Yang-Mills, using crossing symmetry and large spin limits, aligning with existing literature.

Contribution

It introduces a method to predict the structure constant at all loops for large spin operators, based on crossing symmetry and perturbative assumptions.

Findings

Predicted structure constant matches known large j results.

Proposed an expression for the four-point correlator G(u,v) at all loops.

Validated predictions against existing literature results.

Abstract

We analyze the properly normalized three-point correlator of two protected scalar operators and one higher spin twist-two operator in N=4 super Yang-Mills, in the limit of large spin j. The relevant structure constant can be extracted from the OPE of the four-point correlator of protected scalar operators. We show that crossing symmetry of the four point correlator plus a judicious guess for the perturbative structure of the three-point correlator, allow to make a prediction for the structure constant at all loops in perturbation theory, up to terms that remain finite as the spin becomes large. Furthermore, the expression for the structure constant allows to propose an expression for the all loops four-point correlator G(u,v), in the limit u,v -> 0. Our predictions are in perfect agreement with the large j expansion of results available in the literature.