2 research outputs found
Three-point function of semiclassical states at weak coupling
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.Comment: 28 pages, 5 figures, cosmetic changes and more typos corrected in v