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

We start a systematic study of quarter-BPS operators in four-dimensional $$ \mathcal{N} $$ N = 4 Super Yang-Mills with gauge group 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.