Antiferromagnetic Operators in N=4 Supersymmetric Yang-Mills Theory

TL;DR

This paper calculates an upper bound on the scaling dimension of operators in the su(2) sector of N=4 SYM using Bethe ansatz, linking finite operator spectrum with string theory predictions via AdS/CFT.

Contribution

It introduces a method to determine the upper bound on operator scaling dimensions in the large R-charge limit of N=4 SYM using Bethe ansatz techniques.

Findings

Derived an explicit upper bound on scaling dimensions in the su(2) sector.

Confirmed the bounded spectrum aligns with string theory expectations.

Provided a computational approach for analyzing operator spectra in supersymmetric theories.

Abstract

The spectrum of operators in the su(2) sector of N=4 SYM is bounded because the number of operators is finite. According to the AdS/CFT correspondence, the string spectrum in this sector should be also bounded. In this paper the upper bound on the scaling dimension is calculated in the limit of the large R-charge using Bethe ansatz.