Operators with Large R-Charge in N=4 Yang–Mills Theory

Abstract

It has been recently proposed that string theory in the background of a plane wave corresponds to a certain subsector of the N = 4 supersymmetric Yang-Mills theory. This correspondence follows as a limit of the AdS/CFT duality. As a particular case of the AdS/CFT correspondence, it is a priori a strong/weak coupling duality. However, the predictions for the anomalous dimensions which follow from this particular limit are analytic functions of the 't Hooft coupling constant λ and have a well defined expansion in the weak coupling regime. This allows one to conjecture that the correspondence between the strings on the plane wave background and the Yang-Mills theory works at the level of perturbative expansions.In our paper we perform perturbative computations in the Yang-Mills theory that confirm this conjecture. We calculate the anomalous dimension of the operator corresponding to the elementary string excitation. We verify at the two loop level that the anomalous dimension has a finite limit when the R charge J → ∞ keeping λ/J 2 finite. We conjecture that this is true at higher orders of perturbation theory. We show, by summing an infinite subset of Feynman diagrams, under the above assumption, that the anomalous dimensions arising from the Yang-Mills perturbation theory are in agreement with the anomalous dimensions following from the string worldsheet sigma-model.

Planar plane-wave matrix theory at the four loop order: Integrability without BMN scaling

“…We explicitly compute the planar effective Hamiltonian in the su(2) subsector without relying on any 2 In the literature arguments for the mechanism of an all loop BMN scaling property of N = 4 SYM have been put forward in [13]. In particular our finding of the "naive" BMN scaling property is in line with these arguments, the breakdown of BMN scaling arises from subtle boundary effects when two impurities come close to each other to be discussed in section 4.…”

pp-wave light-cone superstring field theory

“…Moreover, the finite quantity ∆−J is a function of λ ′ [20,23,24] and g 2 2 [21,22]. The expansion parameters g 2 and λ ′ are related to string theory parameters by [20] …”

“…While some further investigation seems necessary to clarify the exact form of this correspondence, at the planar (interacting) field theory two-point function/free string level, there is increasing evidence [20,23,24] that the BMN operators do correspond to the free string theory. The extension of the duality beyond this limit, by considering string interactions and the non-planar sector of (interacting) gauge theory respectively, needs further clarification.…”

pp-wave/Yang–Mills correspondence: an explicit check

“…Furthermore, the prefactor v IJ is given 9) where α = α 1 α 2 α 3 . The terms on the second line are irrelevant for supergravity but become important for string states.…”