Metric positivity and the Swampland

by Nicolo Petri (INFN Torino)

Wednesday Mar 12, 2025, 2:00 PM → 3:00 PM Europe/Rome

Aula Galileo

The formulation of abstract notions about physical theories to study their universal features is a typical strategy in modern high-energy physics. In this regard, a widely accepted belief is that geometrical notions, like metrics and distances between vacua configurations of physical theories, should always exist. However, defining a consistent metric and distance between vacua in gravitational theories is an important open problem. In my talk, I will show how this issue is deeply connected to the challenge of formulating scale-separated vacua in string theory. The main goal is to introduce a consistent procedure for defining and computing metrics on the space of gravity vacua, providing a clear way to measure distances. I will then demonstrate how these concepts can be explicitly formulated in N=1 AdS4 orientifold vacua in string theory, a well-known example of scale-separated vacua. The key idea behind this approach involves considering the off-shell quadratic variation of the string theory action and evaluating it over the space of on-shell solutions. Finally, I will discuss how this framework provides new insights into the ongoing debate regarding the consistency of scale-separated vacua in string theory.