The Algebraic Curve of 1-loop Planar N=4 SYM

TL;DR

This paper derives the algebraic curve for the 1-loop planar N=4 SYM using the thermodynamic limit of the algebraic Bethe ansatz, linking gauge theory and string theory via integrability.

Contribution

It explicitly determines the algebraic curve for the psu(2,2|4) spin chain and compares it with semiclassical string configurations, establishing a detailed correspondence.

Findings

Algebraic curve for the psu(2,2|4) spin chain is derived.

Comparison with semiclassical string solutions shows agreement.

Supports integrability-based correspondence between gauge and string theories.

Abstract

The algebraic curve for the psu (2,2|4) quantum spin chain is determined from the thermodynamic limit of the algebraic Bethe ansatz. The Hamiltonian of this spin chain has been identified with the planar 1-loop dilatation operator of N=4 SYM. In the dual AdS_5 x S^5 string theory, various properties of the data defining the curve for the gauge theory are compared to the ones obtained from semiclassical spinning-string configurations, in particular for the case of strings on AdS_5 x S^1 and the su(2,2) spin chain agreement of the curves is shown.