Supergluon scattering in AdS: constructibility, spinning amplitudes, and new structures

We elaborate on a new recursive method proposed in arXiv:2312.15484 for computing tree-level n-point supergluon amplitudes as well as those with one gluon, i.e., spinning amplitudes, in AdS₅ × S³. We present an improved proof for the so-called "constructibility" of supergluon and spinning amplitudes based on their factorizations and flat-space limit, which allows us to determine these amplitudes in Mellin space to all n. We present explicit and remarkably simple expressions for up to $n=7$ supergluon amplitudes and $n=6$ spinning amplitudes, which can be viewed as AdS generalizations of the scalar-scaffolded gluon amplitudes proposed recently. We then reveal a series of hidden structures of these AdS amplitudes including (1) an understanding of general pole structures especially the precise truncation on descendent poles (2) a derivation of simple "Feynman rules" for the all-n amplitudes with the simplest R-symmetry structures, and (3) certain universal behavior analogous to the soft/collinear limit of flat-space amplitudes.