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

Abstract

We consider the matrix model approach to the anomalous dimension matrix in $\mathcal{N}=4$ 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.

24 pages, major changes in most of the paper, conclusions affected

References in corpus (9)

• Spinning strings and AdS/CFT duality
• Large spin limits of AdS/CFT and generalized Landau-Lifshitz equations
• SL(2) spin chain and spinning strings on AdS_5xS^5
• Two-loop commuting charges and the string/gauge duality
• Noncommutative Quantum Scattering in a Central Field
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• Quiver Mechanics for Deconstructed Matrix String
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Cited by in corpus (14)

• Octagons I: Combinatorics and Non-Planar Resummations
• Superstring sigma models from spin chains: the SU(1,1|1) case
• Sigma model from SU(1,1|2) spin chain
• Spin bits at two loops
• Matrix Models
• BPS Condensates, Matrix Models and Emergent String Theory
• Statistical mechanics for dilatations in N=4 super Yang--Mills theory
• On dilatation operator for a renormalizable theory
• Non-planar spin bits beyond two loops
• Random walks in N = 4 Super Yang-Mills
• Dilatation operator or Hamiltonian?
• N-dimensional electron in a spherical potential: the large-N limit
• Dilatation Operator and Space-time Geometry
• Matrix at slow roll: Nonrelativistic and Perturbative