Bootstrapping mixed correlators in $\mathcal{N}=4$ Super Yang-Mills

Understand

We perform a numerical bootstrap study of the mixed correlator system containing the half-BPS operators of dimension two and three in $\mathcal N = 4$ Super Yang-Mills.

• This setup improves on previous works in the literature that only considered single correlators of one or the other operator.
• We obtain upper bounds on the leading twist in a given representation of the R-symmetry by imposing gaps on the twist of all operators rather than the dimension of a single one.
• As a result we find a tension between the large $N$ supergravity predictions and the numerical finite $N$ results already at $N\sim 100$.