Three-point functions of semiclassical string states and conserved currents in AdS_4 x CP^3

In this paper we study the three-point correlation functions of two scalar operators with large conformal dimensions and the R-current or stress-energy tensor at strong coupling with the help of the AdS_4/CFT_3 correspondence. The scalar operators are dual to semiclassical strings in AdS_4 x CP^3, which are point-like in AdS. We establish thorough concordance between string theory results at large coupling constant and general predictions coming from Ward identities in the dual three-dimensional superconformal gauge theory.Comment: 11 pages, no figures, minor changes, references adde

On semiclassical calculation of three-point functions in AdS_4 x CP^3

Recently there has been progress on the computation of two- and three-point correlation functions with two "heavy" states via semiclassical methods. We extend this analysis to the case of AdS_4 x CP^3, and examine the suggested procedure for the case of several simple string solutions. By making use of AdS/CFT duality, we derive the relevant correlation functions of operators belonging to the dual N=6 Chern-Simons gauge theory.Comment: 26 pages, no figures, references adde

Three- and four-point correlators of operators dual to folded string solutions in AdS_5 x S^5

Recently there has been progress on the calculation of n-point correlation functions with two "heavy" (with large quantum numbers) states at strong coupling. We extend these findings by computing three-point functions corresponding to a folded three-spin semiclassical string with one angular momentum in AdS and two equal spins in the sphere. We recover previous results as limiting cases. Also, following a recent paper by Buchbinder and Tseytlin, we provide relevant four-point functions and consider some of their limits.Comment: 19 pages, no figures, minor change

Three-point correlation functions from pulsating strings in AdS5×S5_5\times S^5

One of the most important problems in any conformal field theory is the calculation of three-point functions of primary operators. In this paper we provide explicit examples of correlators with two scalar operators in $\,{\cal N}=4$ super-Yang--Mills theory at large $N$, corresponding to pulsating semiclassical strings in AdS$_5\times S^5$, and an operator with small quantum numbers at strong coupling.Comment: 12 pages, no figures, improvements mad

Three-point correlators: Examples from Lunin-Maldacena background

Recently there has been progress on the calculation of three-point functions with two "heavy" operators via semiclassical methods. We extend this analysis to the case of the Lunin-Maldacena background, and examine the suggested procedure for several simple string solutions. By making use of AdS/CFT duality, we derive the relevant correlation functions of operators belonging to the dual N=1 superconformal gauge theory, and recover an important relation connecting the dimensions of "heavy" states and the structure constants.Comment: 11 pages, no figures, incorrect subsection removed, typos fixed, references added and update

On the pulsating strings in Sasaki-Einstein spaces

We study the class of pulsating strings in AdS_5 x Y^{p,q} and AdS_5 x L^{p,q,r}. Using a generalized ansatz for pulsating string configurations, we find new solutions for this class in terms of Heun functions, and derive the particular case of AdS_5 x T^{1,1}, which was analyzed in arXiv:1006.1539 [hep-th]. Unfortunately, Heun functions are still little studied, and we are not able to quantize the theory quasi-classically and obtain the first corrections to the energy. The latter, due to AdS/CFT correspondence, is supposed to give the anomalous dimensions of operators of the gauge theory dual N=1 superconformal field theory.Comment: 9 pages, talk given at the 2nd Int. Conference AMiTaNS, 21-26 June 2010, Sozopol, Bulgaria, organized by EAC (Euro-American Consortium) for Promoting AMiTaNS, to appear in the Proceedings of 2nd Int. Conference AMiTaN

Semiclassical strings in marginally deformed toric AdS/CFT

We study string solutions in the beta-deformed Sasaki-Einstein gauge/gravity dualities. We find that the BPS point-like strings move in the submanifolds where the two U(1) circles shrink to zero size. In the corresponding T^3 fibration description, the strings live on the edges of the polyhedron, where the T^3 fibration degenerates to T^1. Moreover, we find that for each deformed Sasaki-Einstein manifold the BPS string solutions exist only for particular values of the deformation parameter. Our results imply that in the dual field theory the corresponding BPS operators exist only for these particular values of the deformation parameter we find. We also examine the non-BPS strings, derive their dispersion relations and compare them with the undeformed ones. Finally, we comment on the range of the validity of our solutions and their dependence on the deformation parameter.Comment: 29 pages, 9 figure

Holographic 3-point function at one loop

We explore the recent weak/strong coupling match of three-point functions in the AdS/CFT correspondence for two semi-classical operators and one light chiral primary operator found by Escobedo et al. This match is between the tree-level three-point function with the two semi-classical operators described by coherent states while on the string side the three-point function is found in the Frolov-Tseytlin limit. We compute the one-loop correction to the three-point function on the gauge theory side and compare this to the corresponding correction on the string theory side. We find that the corrections do not match. Finally, we discuss the possibility of further contributions on the gauge theory side that can alter our results.Comment: 24 pages, 2 figures. v2: Typos fixed, Ref. added, figure improved. v3: Several typos and misprints fixed, Ref. updated, figures improved, new section 2.3 added on correction from spin-flipped coherent state, computations on string theory side improve