Three-point correlators of twist-2 operators in N=4 SYM at Born approximation

TL;DR

This paper computes three-point correlators of twist-2 operators in N=4 SYM at leading order, revealing simplifications for large spins and providing new results for correlators involving Konishi operators.

Contribution

It presents the first calculation of specific three-point correlators involving twist-2 operators in N=4 SYM at Born approximation, including cases with arbitrary spins and a correlator with a Konishi operator.

Findings

Correlators simplify when spins are large or zero.

Explicit formulas obtained for arbitrary spins in the Born approximation.

The second correlator involving Konishi operator vanishes at leading order and is computed at g^2 order.

Abstract

We calculate two different types of 3-point correlators involving twist-2 operators in the leading weak coupling approximation and all orders in N_c in N=4 SYM theory. Each of three operators in the first correlator can be any component of twist-2 supermultiplet, though the explicit calculation was done for a particular component which is an SU(4) singlet. It is calculated in the leading, Born approximation for arbitrary spins j_1,j_2,j_3. The result significantly simplifies when at least one of the spins is large or equal to zero and the coordinates are restricted to the 2d plane spanned by two light-rays. The second correlator involves two twist-2 operators Tr X\nabla^{j_1}X +..., Tr Z\nabla^{j_2}Z+... and one Konishi operator Tr[\bar Z,\bar X]^2. It vanishes in the lowest g^0 order and is computed at the leading g^2 approximation.