Three-point function of heavy non-BPS operators in the su(2) sector of N=4 SYM

We derive an 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. The 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-wavelength 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. The result is based on a representation of the Slavnov determinant as a free fermion expectation value, and a subsequent bosonization.