Speaker
Description
Computing the gravitational path integral over Lorentzian geometries presents two key challenges. Firstly, determining the appropriate configurations to include in the path integral, in particular whether to allow for causality-violating configurations. Secondly, the path integrals exhibit high oscillatory behaviour and are defined over unbounded domains, posing difficulties for analytical and numerical computations. In this talk, we explore how these challenges can be effectively addressed employing Picard-Leftschetz methods applied to Regge calculus, a discrete approach to gravity. We introduce the Regge action for complexified variables and examine its analytical continuation, resulting in a unique complex action, except for causality-violating configurations, which manifest as branch cuts. We also highlight on implications and applications to cosmology and effective spinfoam models.
