Celestial Klein spaces

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