Rebooting quarter-BPS operators in $\mathcal{N}=4$ Super Yang-Mills

TL;DR

This paper systematically studies quarter-BPS operators in 4D $ ext{SU}(N)$ $ ext{N}=4$ Super Yang-Mills, utilizing conformal field theory tools to compute protected correlators and analyze large-N supergravity limit data.

Contribution

It adapts embedding space tensor structures and chiral algebra techniques to fix four-point correlators of quarter-BPS operators in $ ext{N}=4$ SYM.

Findings

Fixed the protected part of four-point correlators with minimal ambiguities.

Analyzed leading order OPE data in the large-N supergravity limit.

Connected four-point functions to five-point functions of half-BPS operators.

Abstract

We start a systematic study of quarter-BPS operators in four-dimensional $\mathcal{N}=4$ Super Yang-Mills with gauge group $\mathrm{SU}(N)$ making use of recently developed tools in conformal field theory. We adapt the technology of embedding space tensor structures in four dimensions to the problem of computing R-symmetry tensor structures and we use the underlying chiral algebra to obtain the superconformal Ward identities. This allows us to fix the protected part of the four-point correlators, up to few ambiguities. As applications, we use the Lorentzian inversion formula to study the leading order OPE data in the large~$N$ supergravity limit and we make contact with the OPE limit of the five-point function of half-BPS operators.