Note on KSW-allowability of Wine-Glass Geometry

In this note we consider no-boundary instantons and wine-glass geometries which are of interest in the context of quantum cosmology. While the former usually appears as a dominant saddle in the path-integral, the wineglass geometry can become dominant saddle in some situations. The later has been argued to have a longer inflationary phase of the Universe. Kontsevich-Segal-Witten (KSW)-allowability criterion which classifies geometries on the basis of the requirement of having a meaningful QFT on it, pushes one to analyse the allowability of the various geometries. In this note we do a simple study to seek answer to the allowabilty of no-boundary instantons and wine-glass geometries, where the later is obtained via analytical continuation of Lorentzian deSitter in pure gravity. Our simple analysis which make use of a milder version of KSW allowability criterion shows that no-boundary instanton is KSW allowed while wine-glass geometries obtained via such analytic continuation in pure-gravity are KSW disallowed. This study however doesn't covers wineglass saddles arising in gravity coupled with matter theories.