BPS Operators in N=4 SYM: Calogero Models and 2D Fermions

TL;DR

This paper establishes a connection between protected operators in N=4 super Yang-Mills theory and Calogero models, extending the free fermion description to more general operators and analyzing their symmetries.

Contribution

It generalizes the free fermion description of chiral primary operators to a broader class of protected operators using Calogero models.

Findings

Protected operators charged under su(1|1) are described by the rational super-Calogero model.

Symmetries of these operators contract from Yangian to loop algebra.

The framework applies to operators charged under su(2|3) in the superconformal algebra.

Abstract

A connection between the gauge fixed dynamics of protected operators in superconformal Yang-Mills theory in four dimensions and Calogero systems is established. This connection generalizes the free Fermion description of the chiral primary operators of the gauge theory formed out of a single complex scalar to more general operators. In particular, a detailed analysis of protected operators charged under an su(1|1)contained in psu(2,2|4) is carried out and a class of operators is identified, whose dynamics is described by the rational super-Calogero model. These results are generalized to arbitrary BPS operators charged under an su(2|3) of the superconformal algebra. Analysis of the non-local symmetries of the super-Calogero model is also carried out, and it is shown that symmetry for a large class of protected operators is a contraction of the corresponding Yangian algebra to a loop algebra.