Celestial Klein Spaces

Abstract

We consider the analytic continuation of $(p+q)$-dimensional Minkowski space (with $p$ and $q$ even) to $(p,q)$-signature, and study the conformal boundary of the resulting "Klein space". Unlike the familiar $(-+++..)$ signature, now the null infinity $\mathcal{I}$ has only one connected component. The spatial and timelike infinities ($i^0$ and $i^{\prime }$) are quotients of generalizations of AdS spaces to non-standard signature. Together, $\mathcal{I},i^0$ and $i^{\prime }$ combine to produce the topological boundary $S^{p+q-1}$ as an $S^{p-1}\times S^{q-1}$ fibration over a null segment. The highest weight states (the $L$-primaries) and descendants of $SO(p,q)$ with integral weights give rise to natural scattering states. One can also define $H$-primaries which are highest weight with respect to a signature-mixing version of the Cartan-Weyl generators that leave a point on the celestial $S^{p-1}\times S^{q-1}$ fixed. These correspond to massless particles that emerge at that point and are Mellin transforms of plane wave states.

42 pages, V3: published version