B Euclidean AdS3 path integral and its analytic continuation 15

We consider quantum general relativity in three dimensions with a positive cos-mological constant. The Hartle-Hawking wave function is computed as a function of metric data at asymptotic future infinity. The analytic continuation from Euclidean Anti-de Sitter space provides a natural integration contour in the space of metrics, al-lowing us – with certain assumptions – to compute the wave function exactly, including both perturbative and non-perturbative effects. The resulting wave function is a non-normalizable function of the conformal structure of future infinity which is infinitely peaked at geometries where I+ becomes infinitely inhomogeneous. We interpret this as a non-perturbative instability of de Sitter space in three dimensional Einstein gravity. ar X i