Real observers solving imaginary problems

Abstract: The sphere partition function is one of the simplest euclidean gravity computations. It is usually interpreted as count of states. However, the one loop gravity correction contains a dimension dependent phase factor, $i^{D+2}$, which seems confusing for such an interpretation. We show that, after including an observer, this phase gets mostly cancelled for the quantity that should correspond to a count of states. However, an overall minus sign remains.