On matrix models for anomalous dimensions of super-Yang–Mills theory

2004/10/31 by Stefano Bellucci, Corneliu Sochichiu · 1 citation
Mathematics · Physics and Astronomy · #Action (physics) #Black Holes and Theoretical Physics #Computer science #Dimension (graph theory) #Field (mathematics) #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Matrix (chemical analysis) #Noncommutative and Quantum Gravity Theories #Particle physics theoretical and experimental studies #Path (computing) #Path integral formulation #Physics #Pure mathematics #Quantum mechanics #Representation (politics) #hep-th

paper · pdf · doi:10.1016/j.nuclphysb.2005.07.026

published as Nucl.Phys. B726 (2005) 233-251 · 24 pages, major changes in most of the paper, conclusions affected

arxiv created 2005/07/06 · openalex publication_date 2005/08/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We consider the matrix model approach to the anomalous dimension matrix in N=4 super Yang--Mills theory. We construct the path integral representation for the anomalous dimension density matrix and analyze the resulting action. In particular, we consider the large N limit, which results in a classical field theory. Since the same limit leads to spin chains, we propose to consider the former as an alternative description of the latter. We consider also the limit of small N, which corresponds to the restriction to the diagrams of maximal topological genus.

Citations

• Exercising in K-theory: Brane Condensation without Tachyon
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• String theory and noncommutative geometry
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• Can string bits be supersymmetric?
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• The Dilatation Operator of Conformal N=4 Super Yang-Mills Theory
• The Dilatation Operator of \cal N = 4 SYM and Classical Limits of Spin Chains and Matrix Models
• Mtheory as a matrix model: A conjecture
• A planar diagram theory for strong interactions
• The large N limit of superconformal field theories and supergravity

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• Spin bits at two loops