Physical instabilities and the phase of the Euclidean path integral
摘要
We compute the phase of the Euclidean gravity partition function on manifolds of the form Sp × Mq. We find that the total phase is equal to the phase in pure gravity on Sp times an extra phase that arises from negative mass squared fields that we obtain when we perform a Kaluza-Klein reduction to Sp. The latter can be matched to the phase expected for physical negative modes seen by a static path observer in dSp. In the case of Sp × Sq the answer can be interpreted in terms of a computation in the static patch of dSp or dSq. We also provide the phase when we have a product of many spheres. We clarify the procedure for determining the precise phase factor. We discuss some aspects of the interpretation of this phase.