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

2002/05/31 by David J. Gross, Andrei Mikhailov, Radu Roiban · 196 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Conjecture #Cosmology and Gravitation Theories #Coupling constant #Feynman diagram #Gauge theory #Mathematical physics #Non-critical string theory #Operator product expansion #Particle physics theoretical and experimental studies #Perturbation theory (quantum mechanics) #Physics #Pure mathematics #Quantum electrodynamics #Quantum mechanics #String theory #Supersymmetry #Worldsheet #Yang–Mills theory #hep-th

paper · pdf · doi:10.1006/aphy.2002.6293

published in Annals of Physics 301(1), 31-52 (Elsevier BV) · 26 pages, LaTeX, added references, small changes in the introduction

arxiv created 2002/06/21 · openalex publication_date 2002/10/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

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/J² 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.

Citations

• Open Strings on Plane waves and their Yang-Mills duals
• An exact prediction of N=4 supersymmetric Yang–Mills theory for string theory
• The pp-wave limits of orbifolded AdS5×S5
• Non-renormalization of two and three point correlators of SYM in superspace
• Two-point functions of chiral operators in Script N = 4 SYM at order g4
• A new double-scaling limit of =4 super-Yang–Mills theory and pp-wave strings
• Randall–Sundrum zero mode as a Penrose limit
• The Large-N Limit of Superconformal Field Theories and Supergravity
• The large N limit of superconformal field theories and supergravity

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• Stringing spins and spinning strings
• Higher loops, integrability and the near BMN limit