Three-point function of semiclassical states at weak coupling

TL;DR

This paper derives an analytic expression for the three-point correlation function of heavy operators in N=4 super-Yang-Mills theory at weak coupling, using Bethe Ansatz techniques and a fermionic-bosonic reformulation.

Contribution

It provides a novel factorized operator expression for scalar products of Bethe states, connecting integrable spin chain methods to gauge theory correlators.

Findings

Explicit formula for three-point functions of heavy operators

Application of Bethe Ansatz and fermionic-bosonic reformulation

Connection between spin chain excitations and classical string states

Abstract

We give the derivation of the previously announced analytic expression for the correlation function of three heavy non-BPS operators in N=4 super-Yang-Mills theory at weak coupling. The three operators belong to three different su(2) sectors and are dual to three classical strings moving on the sphere. Our computation is based on the reformulation of the problem in terms of the Bethe Ansatz for periodic XXX spin-1/2 chains. In these terms the three operators are described by long-wave-length excitations over the ferromagnetic vacuum, for which the number of the overturned spins is a finite fraction of the length of the chain, and the classical limit is known as the Sutherland limit. Technically our main result is a factorized operator expression for the scalar product of two Bethe states. The derivation is based on a fermionic representation of Slavnov's determinant formula, and a subsequent bosonisation.