AdS super gluon scattering up to two loops: A position space approach

We carry out a bootstrap study of four-point correlators in 4d $\mathcal{N}=2$ SCFTs which are dual to super Yang-Mills on $AdS_5\times S^3$. We focus on the simplest $\frac{1}{2}$-BPS operators which correspond to the super gluons in the massless current multiplet. Our computation is based on an ansatz in position space which is inspired by a hidden symmetry structure manifest in the leading terms of the Lorentzian singularities of the correlators. By using other consistency conditions, we completely fix the super gluon correlators at one and two loops in the bulk genus expansion, up to possible counterterms. Our results reveal a number of interesting properties enriched by the color structures. In particular, the implication of hidden conformal symmetry on the full super gluon reduced correlator exhibits an analogous pattern as in the $AdS_5\times S^5$ supergravity correlators recently computed up to two loops.