Holography of Two-Point Functions in the Spinning String/Spin Chain Correspondence

Abstract

We study the holographic principle of the two-point function in the case of a spinning string in the AdS/CFT correspondence. Following the general method proposed by Yoneya et al. for the bulk-boundary correspondence in the large J limit, we study the spinning string solution which starts and ends at the boundary. We then show that the spinning string solution directly gives a two-point function that is consistent with the spin chain picture in gauge theory. * )

One-point functions in AdS/dCFT from matrix product states

“…The classical solution for the latter is the Euclidean continuation of the BMN geodesic [41][42][43]:…”

Holographic three-point functions of semiclassical states

“…They can be obtained by the Euclidean continuation of spinning strings in global AdS. In the Poincaré patch the string worldsheet indeed collapses onto the boundary at two points [16,17,23]. Constructing solutions dual to three-point functions seems to be a difficult problem.…”

Correlators of massive string states with conserved currents

“…The result obtained this way disagrees with the result calculated in the supergravity approximation [38] when the charges of the two "heavy" BPS states are extrapolated to very large values. This is so because the supergravity approximation is not a priori valid if the charges of the supergravity states 11 By light we mean operators with conformal dimensions ∆ << √ λ.…”

“…Recently, another approach to the calculation of n-points correlators involving non-BPS states was developed [11][12][13][14][15]. More precisely, the authors of [12] argued that it should be possible to obtain the correlation functions of local operators corresponding to classical spinning string states, at strong coupling, by evaluating the string action on a classical solution with appropriate boundary conditions after convoluting with the relevant to the classical states wavefunctions.…”