Spin Chain for Quantum Strings

TL;DR

Problem: understand how integrable structures in N=4 SYM and strings on AdS5×S5 relate through Bethe Ansatz descriptions in the SU(2) subsector. Approach: compare gauge-theory and string-theory Bethe equations and derive a perturbative spin-chain Hamiltonian at weak coupling, introducing a tunable parameter $c_4$. Findings: gauge theory is recovered with $c_4=0$, while matching the string Bethe equations requires $c_4=1$, with higher-loop coefficients fixed accordingly; multiple state checks support the correspondence. Significance: clarifies the perturbative relationship between gauge and string integrability, highlights wrapping/thermodynamic-limit issues, and points to whether a string-based spin chain can describe the theory beyond leading orders.

Abstract

We review and compare the integrable structures in N=4 gauge theory and string theory on AdS5xS5. Recently, Bethe ansaetze for gauge theory/weak coupling and string theory/strong coupling were proposed to describe scaling dimensions in the su(2) subsector. Here we investigate the Bethe equations for quantum string theory, naively extrapolated to weak coupling. Excitingly, we find a spin chain Hamiltonian similar, but not equal, to the gauge theory dilatation operator.