The Dilatation Operator of $\mathcal{N}$ $=$ 4 SYM and Classical Limits of Spin Chains and Matrix Models

Abstract

A study of the one loop dilatation operator in the scalar sector of $\mathcal{N}$ $=$ 4 SYM is presented. The dilatation operator is analyzed from the point of view of Hamiltonian matrix models. A Lie algebra underlying operator mixing in the planar large $N$ limit is presented, and its role in understanding the integrability of the planar dilatation operator is emphasized. A classical limit of the dilatation operator is obtained by considering a contraction of this Lie algebra, leading to a new way of constructing classical limits for quantum spin chains. An infinite tower of local conserved charges is constructed in this classical limit purely within the context of the matrix model. The deformation of these charges and their relation to the charges of the spin chain is also elaborated upon.

20 Pages, 3 figures. Typos corrected and references added in the replacement

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Cited by in corpus (19)

• Bethe Ansatz for Quantum Strings
• Integrable Hamiltonian for Classical Strings on AdS_5 x S^5
• Deformations of N=4 SYM and integrable spin chain models
• Nucleon isovector structure functions in (2+1)-flavor QCD with domain wall fermions
• Yang-Mills Correlation Functions from Integrable Spin Chains
• Bethe Ansatz for a Quantum Supercoset Sigma Model
• One-Loop QCD Spin Chain and its Spectrum
• Yangian Symmetries of Matrix Models and Spin Chains: The Dilatation Operator of $\mathcal{N}$$=4$ SYM
• The algebra of flat currents for the string on AdS_5 x S^5 in the light-cone gauge
• Yangians, S-matrices and AdS/CFT
• Circular and Folded Multi-Spin Strings in Spin Chain Sigma Models
• On matrix models for anomalous dimensions of super Yang-Mills theory
• Matrix Models
• Review of AdS/CFT Integrability, Chapter VI.2: Yangian Algebra
• BPS Condensates, Matrix Models and Emergent String Theory
• Statistical mechanics for dilatations in N=4 super Yang--Mills theory
• Random walks in N = 4 Super Yang-Mills
• Mass-Gaps and Spin Chains for (Super) Membranes
• Large-N Limit as a Classical Limit: Baryon in Two-Dimensional QCD and Multi-Matrix Models