Classical/quantum integrability in non-compact sector of AdS/CFT

TL;DR

This paper explores the integrable structures of non-compact SL(2,R) sectors in N=4 SYM and AdS string theory, establishing a connection between classical sigma models and Bethe equations at one loop.

Contribution

It formulates and solves the Riemann-Hilbert problem for finite gap solutions, linking classical sigma models to spin chain Bethe equations in the AdS/CFT context.

Findings

Riemann-Hilbert problem solved for finite gap solutions

Identical structure at one loop between sigma model and Bethe equations

Established correspondence between classical and quantum integrability in the non-compact sector

Abstract

We discuss non-compact SL(2,R) sectors in N=4 SYM and in AdS string theory and compare their integrable structures. We formulate and solve the Riemann-Hilbert problem for the finite gap solutions of the classical sigma model and show that at one loop it is identical to the classical limit of Bethe equations of the spin (-1/2) chain for the dilatation operator of SYM.