Abstract
Scattering amplitudes of massless particles in Minkowski space can be expressed in a conformal basis by Mellin transforming the momentum space amplitudes to correlation functions on the celestial sphere at null infinity. In this paper, we study celestial amplitudes of loop level gluons and gravitons. We focus on the rational amplitudes that carry all-plus and single-minus external helicities. Because these amplitudes are finite, they provide a concrete example of celestial amplitudes of Yang- Mills and gravity theory beyond tree level. We give explicit examples of four and five point functions and comment on higher point amplitudes.
Highlights
The scattering amplitudes in Minkowski space can be mapped to the celestial sphere at lightlike infinity, where they are encoded in terms of conformal correlators [1]
This observation provides a complementary representation of scattering amplitudes where they are beheld as a holographically dual conformal field theory residing in the celestial sphere
The holographic nature of celestial amplitudes in principle can shine light on an outstanding problem, i.e., what is a concrete holographic formulation for flat spacetime?1 More terrestrially, one can view celestial amplitude much in the same way as twistors, momentum twistors, and scattering equations, which may help in illuminating hidden mathematical structures in quantum field theory that were not previously accessible from traditional calculations [11]
Summary
The scattering amplitudes in Minkowski space can be mapped to the celestial sphere at lightlike infinity, where they are encoded in terms of conformal correlators [1]. While scalar loops have been studied in [18], most construction of celestial amplitudes have occurred at tree level. It is a well known result that gluon as well as graviton amplitudes at tree level vanish for all-positive and one-minus external states [39]. For one loop, one cannot construct such amplitudes using unitarity cuts in four dimensions as a two particle cut leads to tree-level expressions with at least one vanishing piece. These one-loop amplitudes when integrated are relatively simple rational functions and contain no logarithmic divergences in four dimensions.. We end with future directions and a conclusion, and collected several technical details in the Appendix A
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