Higher loops, integrability and the near BMN limit

2003/08/11 by Niklas Beisert · 67 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Conjecture #Generator (circuit theory) #Limit (mathematics) #Operator (biology) #Operator product expansion #Particle physics theoretical and experimental studies #Planar #Quantum Chromodynamics and Particle Interactions #Scalar (mathematics) #String theory #hep-th

paper · pdf · doi:10.1088/1126-6708/2003/09/062

published in Journal of High Energy Physics 2003(09), 062 (Springer Nature) · 6 pages

arxiv created 2003/08/11 · openalex publication_date 2003/09/26 · arxiv updated 2011/03/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

In this note we consider higher-loop contributions to the planar dilatation operator of N=4 SYM in the su(2) subsector of two complex scalar fields. We investigate the constraints on the form of this object due to interactions of two excitations in the BMN limit. We then consider two scenarios to uniquely fix some higher-loop contributions: (i) Higher-loop integrability fixes the dilatation generator up to at least four-loops. Among other results, this allows to conjecture an all-loop expression for the energy in the near BMN limit. (ii) The near plane-wave limit of string theory and the BMN correspondence fix the dilatation generator up to three-loops. We comment on the difference between both scenarios.

Citations

• Strings in the near plane wave background and AdS/CFT
• The Dilatation Operator of Conformal N=4 Super Yang-Mills Theory
• BMN operators and superconformal symmetry
• Operators with Large R-Charge in N=4 Yang–Mills Theory
• Exact anomalous dimensions of N=4 Yang–Mills operators with large R charge

Cited by

• The (2|3) dynamic spin chain