Analytic continuation from Minkowski space to (2, 2) split signature spacetime has proven to be a powerful tool for the study of scattering amplitudes. Here we show that, under this continuation, null infinity becomes the product of a null interval with a celestial torus (replacing the celestial sphere) and has only one connected component. Spacelike and timelike infinity are time-periodic quotients of AdS3. These three components of infinity combine to an S3 represented as a toric fibration over the interval. Privileged scattering states of scalars organize into SL(2, ℝ)L ×SL(2, ℝ)R conformal primary wave functions and their descendants with real integral or half-integral conformal weights, giving the normally continuous scattering problem a discrete character.
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ArXiv ePrint: 2101.09591
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Atanasov, A., Ball, A., Melton, W. et al. (2, 2) Scattering and the celestial torus. J. High Energ. Phys. 2021, 83 (2021). https://doi.org/10.1007/JHEP07(2021)083