(2,2) Scattering and the celestial torus

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 AdS(3). These three components of infinity combine to an S-3 represented as a toric fibration over the interval. Privileged scattering states of scalars organize into SL(2, )(L)xSL(2, )(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.

Automated summary

The analytic continuation from Minkowski space to (2,2) split signature spacetime is a powerful tool for studying scattering amplitudes. Under this continuation, null infinity is represented as the product of a null interval and a celestial torus, with only one connected component. Spacelike and timelike infinity are periodic quotients of AdS(3), combining to form an S-3 represented as a toric fibration over the interval. Scattering states of scalars are organized into conformal primary wave functions and their descendants, giving the scattering problem a discrete character.