One-loop gluon amplitudes in AdS

We initiate the study of one-loop gluon amplitudes in AdS space. These amplitudes were recently computed at tree level for a variety of backgrounds of the form AdS d +1 × S 3 . For concreteness, we compute the one-loop correction to the massless gluon amplitude on AdS 5 ×S 3 , which corresponds to the four-point correlator of the flavor current multiplet in the dual 4d 𝒩 = 2 SCFT. This requires solving a mixing problem that involves tree-level amplitudes of arbitrarily massive Kaluza-Klein modes. The final answer has the same color structure as in flat space but the dependence on Mandelstam variables is more complicated, with logarithms replaced by polygamma functions.