Spin chains and gauge-string duality

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.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 2, pp. 179–196, February, 2005.