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arXiv · 2101.09591

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

Alexander Atanasov·Adam Ball·Walker Melton·Ana-Maria Raclariu·Andrew Strominger
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Abstract

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 $SL(2,\mathbb{R})_L \times SL(2,\mathbb{R})_R$ 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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Alexander Atanasov, Adam Ball, Walker Melton, Ana-Maria Raclariu, Andrew Strominger. 2021-01-23. $(2,2)$ Scattering and the Celestial Torus. https://doi.org/10.1007/jhep07(2021)083

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