BMN gauge theory as a quantum mechanical system

2002/12/31 by N. Beisert, C. Kristjansen, J. Plefka +1 · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Conjecture #Dimension (graph theory) #Eigenvalues and eigenvectors #Gauge theory #Hamiltonian (control theory) #Quantum #Quantum Chromodynamics and Particle Interactions #Quantum many-body systems #Scalar (mathematics) #hep-th

paper · pdf · doi:10.1016/s0370-2693(03)00269-7

published as Phys.Lett.B558:229-237,2003 · 13 pages, v2: minor changes, v3: typo corrected, to appear in Phys. Lett. B

arxiv created 2003/03/18 · openalex publication_date 2003/03/26 · arxiv updated 2011/03/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We rigorously derive an effective quantum mechanical Hamiltonian from N=4 gauge theory in the BMN limit. Its eigenvalues yield the exact one-loop anomalous dimensions of scalar two-impurity BMN operators for all genera. It is demonstrated that this reformulation vastly simplifies computations. E.g. the known anomalous dimension formula for genus one is reproduced through a one-line calculation. We also efficiently evaluate the genus two correction, finding a non-vanishing result. We comment on multi-trace two-impurity operators and we conjecture that our quantum-mechanical reformulation could be extended to higher quantum loops and more impurities.

Citations

• BMN correlators and operator mixing in super-Yang–Mills theory
• A new double-scaling limit of =4 super-Yang–Mills theory and pp-wave strings
• Operators with Large R-Charge in N=4 Yang–Mills Theory
• Exact anomalous dimensions of N=4 Yang–Mills operators with large R charge

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