Spin Chains and Gauge/String Duality

TL;DR

This paper explores the connection between integrable spin chains in Yang-Mills theory and their string theory duals, proposing a discretized worldsheet model linked to the spin chain representations.

Contribution

It introduces a novel interpretation of the one-loop dilatation operator using two-point functions on a 2D worldsheet and relates the discretization of the worldsheet to finite gauge coupling effects.

Findings

Expressed the one-loop dilatation operator via 2D worldsheet correlators

Linked the Neumann integrable system to spin chains and worldsheet discretization

Proposed a string bit model as a discretized worldsheet representation

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.