Semiclassical correlators of three states with largeS5charges in string theory inAdS5×S5

Abstract

We consider semiclassical computation of 3-point correlation functions of (BPS or non-BPS) string states represented by vertex operators carrying large charges in S 5 . We argue that the AdS 5 part of the construction of relevant semiclassical solution involves two basic ingredients: (i) configuration of three glued geodesics in AdS 2 suggested by Klose and McLoughlin in arXiv:1106.0495 and (ii) a particular Schwarz-Christoffel map of the 3-geodesic solution in cylindrical (τ, σ) domain into the complex plane with three marked points. This map is constructed using the expression for the AdS 2 string stress tensor which is uniquely determined by the 3 scaling dimensions ∆ i as noted by Janik and Wereszczynski in arXiv:1109.6262 (our solution, however, is different from theirs). We also find the S 5 part of the solution and thus the full expression for the semiclassical part of the 3-point correlator for several examples: extremal and non-extremal correlators of BPS states and a particular correlator of "small" circular spinning strings in S 3 ⊂ S 5 . We demonstrate that for the BPS correlators the results agree with the large charge limit of the corresponding supergravity and free gauge theory expressions. * e.buchbinder@imperial.ac.uk † Also at Lebedev Institute, Moscow. tseytlin@imperial.ac.uk

Computing three-point functions for short operators

“…The intersection point is calculable [21,29], and after including the contributions of the fluctuations one finds the coefficient in front of G 123 in (1.3). For large R-charges J i ≫ 1 we can also use a semiclassical approximation for the S 5 overlap integrals ψ J 1 ψ J 2 ψ J 3 [21,32]. In this approximation we assume that the R-charges are each highest weight with respect to some basis and satisfy…”

ON SEMICLASSICAL CALCULATION OF THREE-POINT FUNCTIONS IN AdS5×T1, 1

“…The approach based on insertion of vertex operators was put forward in Ref. [19,25] where the authors also suggested that the same method applies to higher npoint correlation functions with two "heavy" and n-2 "light" operators. Namely, the semiclassical expression for n-point correlator should be given by a product of "light" vertex operators calculated on the worldsheet surface determined by the "heavy" operator insertions.…”

“…In order to find an explicit solution to the conserved charges (25) we insert the solution (48) to the relations for charges (25), and using the relation (47) we obtain…”

Holographic three-point functions for short operators

“…These include the semi-classical results for two "heavy" and one "light" operator [8,9], three heavy operators [10][11][12], BMN operators with large charges [13], Wilson loops [14] and various other configurations [15]. At weak coupling there has also been some significant results using the Bethe ansatz [16,17].…”