One-loop Gluon Amplitudes in AdS

TL;DR

This paper explores one-loop gluon amplitudes in Anti-de Sitter space, extending tree-level results to include quantum corrections and revealing complex variable dependencies with special functions.

Contribution

It introduces the first computation of one-loop gluon amplitudes in AdS space, involving mixing of Kaluza-Klein modes and complex analytic structures.

Findings

One-loop corrections involve polygamma functions replacing logarithms.

The amplitude maintains flat space color structure.

Complex dependence on Mandelstam variables is characterized.

Abstract

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 $AdS_{d+1} \times S^3$. For concreteness, we compute the one-loop correction to the massless gluon amplitude on $AdS_5\times S^3$, which corresponds to the four-point correlator of the flavor current multiplet in the dual 4d $\mathcal{N}=2$ 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.