Spin Chains and Gauge/String Duality

TL;DR

The paper investigates the stringy origin of integrable spin chains governing operator evolution in N=4 SYM and proposes that the one-loop dilatation operator can be expressed via two-point functions on a 2D worldsheet. It connects weak-coupling gauge theory to a discretized worldsheet through a relation to the Neumann system and argues that discretization yields a string-bit representation of separated variables; at strong coupling, discretized strings map to XYZ spin chains. Separation of variables is interpreted as a string-bit decomposition, with the Baxter equation encoding the single-bit wavefunction and the spectral curve quantization. Together, these results provide a unified picture tying spin-chain integrability, 2D gravitational/gauge structures, and worldsheet discretization within gauge/string duality.

Abstract

The stringy picture behind the integrable spin chains governing the evolution equations in Yang-Mills theory is discussed. It is shown that one-loop dilatation operator in N=4 theory can be expressed in terms of two-point functions on 2d worldsheet. Using the relation between Neumann integrable system and the spin chains it is argued that the transition to the finite gauge theory coupling implies the discretization of the worldsheet. We conjecture that string bit model for the discretized worldsheet corresponds to the representation of the integrable spin chains in terms of the separated variables.