Algebraic Curve for the SO(6) sector of AdS/CFT

TL;DR

This paper constructs the algebraic curve for the SO(6) sector of the AdS/CFT correspondence, matching known results up to two loops and providing explicit solutions, advancing the understanding of integrable structures in this duality.

Contribution

The paper introduces a general algebraic curve for the classical sigma model on R x S^5, connecting it with the dual scalar sector in N=4 SYM and providing explicit solutions.

Findings

Algebraic curve of degree four constructed for the sigma model.

Up to two loops, the curve matches the dual scalar sector in N=4 SYM.

Explicit solutions of the algebraic curve are provided.

Abstract

We construct the general algebraic curve of degree four solving the classical sigma model on RxS5. Up to two loops it coincides with the algebraic curve for the dual sector of scalar operators in N=4 SYM, also constructed here. We explicitly reproduce some particular solutions.