The AdS4/CFT3 algebraic curve

TL;DR

This paper constructs an algebraic curve for the AdS4/CFT3 duality that captures classical string solutions and the spectrum of gauge operators at different coupling regimes, providing a comprehensive tool for spectral analysis.

Contribution

It introduces an algebraic curve framework for AdS4/CFT3 that unifies classical and quantum spectral computations, extending previous methods.

Findings

Encodes all classical string solutions at strong coupling.

Determines the two-loop spectrum of gauge operators at weak coupling.

Allows semi-classical spectrum calculations around any classical solution.

Abstract

We present the OSp(2,2|6) symmetric algebraic curve for the AdS4/CFT3 duality recently proposed in arXiv:0806.1218. It encodes all classical string solutions at strong t'Hooft coupling and the full two loop spectrum of long single trace gauge invariant operators in the weak coupling regime. This construction can also be used to compute the complete superstring semi-classical spectrum around any classical solution. We exemplify our method on the BMN point-like string.