Review of AdS/CFT Integrability, Chapter I.2: The spectrum from perturbative gauge theory

TL;DR

This review discusses the computation of the spectrum of composite operators in N=4 SYM's SU(2) sector using perturbative gauge theory, highlighting multi-loop calculations and wrapping corrections.

Contribution

It provides a detailed analysis of the dilatation operator and spectrum calculations beyond one loop, including the first steps to incorporate wrapping effects.

Findings

Dilatation operator determines spectrum asymptotically beyond four loops.

Explicit Feynman graph calculations confirm spectrum predictions.

Leading wrapping corrections are beginning to be understood.

Abstract

We review the constructions and tests of the dilatation operator and of the spectrum of composite operators in the flavour SU(2) subsector of N=4 SYM in the planar limit by explicit Feynman graph calculations with emphasis on analyses beyond one loop. From four loops on, the dilatation operator determines the spectrum only in the asymptotic regime, i.e. to a loop order which is strictly smaller than the number of elementary fields of the composite operators. We review also the calculations which take a first step beyond this limitation by including the leading wrapping corrections.