Abstract
We analyse the flat space limit of 3-point correlators in momentum space for general conformal field theories in even spacetime dimensions, and show they exhibit a double copy structure similar to that found in odd dimensions. In even dimensions, the situation is more complicated because correlators contain branch cuts and divergences which need to be renormalised. We describe the analytic continuation of momenta required to extract the flat space limit, and show that the flat space limit is encoded in the leading singularity of a 1-loop triangle integral which serves as a master integral for 3-point correlators in even dimensions. We then give a detailed analysis of the renormalised correlators in four dimensions where the flat space limit of stress tensor correlators are controlled by the coefficients in the trace anomaly.
Highlights
Over the past few decades, the study of scattering amplitudes and conformal correlation functions has revealed remarkable new insight into the structure of quantum field theory and quantum gravity
The flat space limit of correlators in general even dimensions can be deduced by applying the appropriate differential operators to the master integral, and we discover the same double copy structure that we previously found in odd dimensions
We extended to even spacetime dimensions our results for the double copy structure of momentumspace conformal field theory (CFT) correlators [16]
Summary
Over the past few decades, the study of scattering amplitudes and conformal correlation functions has revealed remarkable new insight into the structure of quantum field theory and quantum gravity. Euclidean 3-point correlators of stress tensors, conserved currents and marginal scalars were shown to reduce to gauge and gravitational scattering amplitudes in one higher dimension in the flat space limit This was achieved by working in momentum space and taking the energy (defined as the sum of the magnitudes of the three momenta) to zero. IV we use this result to deduce the flat space limit of correlators of stress tensors, currents and marginal scalars in general even dimensions by applying certain differential operators This reveals double copy structure similar to that previously found in odd dimensions. In the Appendix we compute the leading singularity of the master integral
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