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 AdSd+1× S3. For concreteness, we compute the one-loop correction to the massless gluon amplitude on AdS5×S3, 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.
Highlights
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
When computing one-loop correlators, we will focus on the reduced Mellin amplitudes which have already taken into account superconformal symmetry
As we show in appendix C, any Mellin amplitude which has the form of Bs5td and coefficients with the following scaling behavior c5mdn in the large m, n limit, becomes the D-dimensional scalar one-loop box diagram in flat space
Summary
We study scattering amplitudes of super gluons in AdS5. Such super gluons can arise in two basic setups. The 7-brane is located at the slice θ = 0, which fills the AdS5 and occupies an S3 in the compact space On this singular locus, there is a 7+1 dimensional N = 1 vector multiplet which transforms in the adjoint representation of a gauge group GF. The low energy degrees of freedom on the D7-branes are again described by an eight dimensional N = 1 vector multiplet which transforms in the adjoint representation of a gauge group SU(NF ) Reducing this multiplet onto AdS5 leads to the same spectrum of super gluons. The treelevel super gluon exchange amplitude of the lowest Kaluza-Klein mode remains the same after the truncation We will use this truncated theory as a toy model when studying the super gluon amplitudes at one loop
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