On semiclassical approximation and spinning string vertex operators in AdS5×S5

Abstract

Following earlier work by Polyakov and Gubser, Klebanov and Polyakov, we attempt to clarify the structure of vertex operators representing particular string states which have large ("semiclassical") values of AdS energy or 4-d dimension E = ∆ and angular momentum J in S 5 or spin S in AdS 5 . We comment on the meaning of semiclassical limit in the context of α ′ ∼ 1 √ λ perturbative expansion for the 2-d anomalous dimensions of the corresponding vertex operators. We consider in detail the leading-order 1-loop renormalization of these operators in AdS 5 × S 5 sigma model (ignoring fermionic contributions). We find more examples of operators (in addition to the one in hep-th/0110196) for which the 1-loop anomalous dimension can be made small by tuning quantum numbers. We also comment on a possibility of deriving the semiclassical relation between ∆ and J or S from the marginality condition for the vertex operators, using a stationary phase approximation in the path integral expression for their 2-point correlator on a complex plane.

Semiclassical correlation functions of Wilson loops and local vertex operators

“…11) 6 An identical transformation property holds also for the more general case of correlation functions involving the nondegenerate Wilson loop surfaces studied in [34]. This is a consequence of the fact that under the inversion symmetry of the AdS metric the constraint (2.5) maps into itself with the constant p replaced by −p on the right-hand side.…”

“…[6][7][8][9]. The extension to correlation functions with two complex conjugate heavy vertex operators and one light string state with fixed conserved charges was recently proposed in [10][11][12] and has been exhaustively analyzed for a large variety of heavy vertices and light string states [13][14][15][16][17][18][19][20].…”

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

“…To find the stationary point trajectory [2,8,9,16] we may start with the euclidean version of the corresponding classical solution on the cylinder (τ, σ) which carries the same charges as the vertex operators and then transform this solution to the complex ξ-plane by the conformal map…”

“…One may then try to reproduce the expected large charge limit of C using semiclassical string theory arguments. As the semiclassical limit of the 2-point correlator of BPS operators is determined by a euclidean continuation of a massless geodesic in AdS 5 × S 5 [1,[8][9][10] one may expect that in this case the relevant semiclassical trajectory should be given by an intersection of the three geodesics [5] (with an intersection point being in the bulk of AdS 5 in the non-extremal case of ∆ 1 = ∆ 2 + ∆ 3 . )…”

The pomeron in closed bosonic string theory

“…Following [7], [8] we assume that at the lowest order in the world-sheet perturbation theory, the worldsheet supersymmetry as well the Ramond-Ramond fluxes do not make any contribution. So in the following the dynamics will be given by the non-linear σ-model…”