Physics

Scattering amplitude

Pure mathematics

Mathematics

Mathematical physics

Torus

Analytic continuation

Mathematical analysis

Celestial sphere

Null (SQL)

Scattering

Geometry

Computer science

Astrophysics

Quantum mechanics

Conformal map

Infinity

Database

Minkowski space

Journal of High Energy Physics

A bstract 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 , 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.

(2, 2) Scattering and the celestial torus