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Spin chains and gauge-string duality. (English) Zbl 1178.81221

Theor. Math. Phys. 142, No. 2, 153-165 (2005); translation from Teor. Mat. Fiz. 142, No. 2, 179-196 (2005).
Summary: We discuss the string picture behind the integrable spin chains governing the evolution equations in the Yang-Mills theory. We show that the one-loop correction to the dilatation operator in the \(N=4\) theory can be expressed in terms of two-point correlation functions on the two-dimensional worldsheet. Using the relation between the Neumann integrable system and spin chains, we argue that the transition to the finite gauge-theory coupling implies discretization of the worldsheet. We conjecture that the string-bit model for the discretized worldsheet corresponds to the representation of the integrable spin chains in terms of the separated variables.

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T13 Yang-Mills and other gauge theories in quantum field theory
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
81T60 Supersymmetric field theories in quantum mechanics
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