Holographic three-point correlators in the Schrodinger/dipole CFT correspondence

Abstract

We calculate, for the first time, three-point correlation functions involving "heavy" operators in the Schrodinger/null-dipole CFT correspondence at strong coupling. In particular, we focus on the three-point functions of the dilaton modes and two "heavy" operators. The heavy states are dual to the single spin and dyonic magnon, the single spin and dyonic spike solutions or to two novel string solutions which do not have an undeformed counterpart. Our results provide the leading term of the correlators in the large λ expansion and are in perfect agreement with the form of the correlator dictated by non-relativistic conformal invariance. We also specify the scaling function which can not be fixed by using conformal invariance. arXiv:1806.08181v1 [hep-th]

String theory on the Schrödinger pp-wave background

“…These results are the first in the literature where the heavy states described by extended string solutions participate in three-point correlation functions. The results of [51] give the leading term of the correlators in the large λ expansion and are in complete agreement with the form of the correlator dictated by non-relativistic conformal invariance. Finally, pulsating strings solutions in the Schrödinger background were recently found in [52].…”

“…The energies of the string excitations provide the exact in the effective coupling λ ′ = λ J 2 dimensions of certain operators which have large R-charge equal to J. In section 4, we show that two of the eigenfrequencies of the bosonic spectrum derived in the previous section are in complete agreement with the dispersion relation of the giant magnon solution in the original background [47,51], that is before taking the pp-wave limit. Subsequently, inspired by the pp-wave spectrum we conjecture an exact in the t'Hooft coupling dispersion relation for the magnons in the original Schrödinger background.…”

“…We use the Brinkmann form of the background to analyze the spectrum which will be possible to explicitly compute, despite the explicit dependence of the metric coefficients on the coordinate u. The aim is to compare the eigenfrequencies with the dispersion relation of the giant magnon in the initial background (see [47,51]) in the common range of validity.…”

“…Subsequently, the Schrödinger background was utilized in order to calculate, using holography, three-point functions involving two heavy operators and a light one [51].…”

Giant gravitons on the Schrödinger pp-wave geometry

“…Subsequently, three-point correlation functions involving two heavy operators and a light one were calculated in [39] using holography. The light operator was chosen to be one of the modes of the dilaton while the heavy states were chosen to be generalizations of the giant magnon or spike solutions that were constructed in [30].…”