Analytic continuation from Minkowski space to signature spacetime

$(2,2)$ Scattering and the Celestial Torus

We show that null infinity becomes the product of a null interval with a celestial torus (replacing the celestialsphere) and has only one connected component.Spacelike and timelike infinity are time-periodic quotients of timelike infinity.These three components of infinity combine to an represented as a toric fibration over the interval.privileged scattering states of scalars organize into conformal primary wave functions and their descendants with real integral or half-integral conformal weights, giving the normally continuous scattering problem a discrete character.