AdS$_4$/CFT$_3$ for Unprotected Operators

Understand

We consider the four-point function of the lowest scalar in the stress-energy tensor multiplet in $\mathcal{N}=8$ ABJ(M) theory \cite{Aharony:2008ug, Aharony:2008gk}.

• At large central charge $c_T\sim N^{3/2}$, this correlator is given by the corresponding holographic correlation function in 11d supergravity on $AdS_4\times S^7$.
• We use Mellin space techniques to compute the leading $1/c_T$ correction to anomalous dimensions and OPE coefficients of operators that appear in this holographic correlator.
• For half and quarter-BPS operators, we find exact agreement with previously computed localization results.