Constructibility of AdS Supergluon Amplitudes.

We prove that all tree-level n-point supergluon (scalar) amplitudes in AdS_{5} can be recursively constructed, using factorization and flat-space limit. Our method is greatly facilitated by a natural R-symmetry basis for planar color-ordered amplitudes, which reduces the latter to "partial amplitudes" with simpler pole structures and factorization properties. Given the n-point scalar amplitude, we first extract spinning amplitudes with n-2 scalars and one gluon by imposing "gauge invariance," and then use a special "no-gluon kinematics" to determine the (n+1)-point scalar amplitude completely (which in turn contains the n-point single-gluon amplitude). Explicit results of up to 8-point scalar amplitudes and up to 6-point single-gluon amplitudes are included as Supplemental Material.