One-loop Gluon Amplitudes in AdS

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 $Ad{S}_{d+1}\times S^3$. For concreteness, we compute the one-loop correction to the massless gluon amplitude on $Ad{S}_5\times S^3$, 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.

v1: 37 pages, 5 figures, v2: minor improvements, published version, v3: a typo in (2.8) corrected

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• BCJ relations in ${AdS}_5\times S^3$ and the double-trace spectrum of super gluons
• Analytical evaluation of AdS${}_4$ Witten diagrams as flat space multi-loop Feynman integrals
• AdS super gluon scattering up to two loops: A position space approach
• Spinning correlators in $\mathcal{N}=2$ SCFTs: Superspace and AdS amplitudes
• Holographic S-fold theories at one loop
• Scattering bound states in AdS
• 4D Flat-space scattering amplitude /$CF{T}_3$ correlator correspondence revisited
• Information Geometry and Holographic Correlators
• Constructing CFTs from AdS flows