Amineh Mohseni - Measuring Distances in the Quantum Gravity Landscape

In this talk, I present our proposal for a generalized notion of distance between vacua in the theory of a scalar field, $\phi$, with scalar potential $V(\phi)$ coupled to gravity. We propose the normalized tension of a domain wall connecting different field values, with a varying normalization relative to a local energy scale, as the measure of distance. We show that this definition reproduces the usual moduli space distance for a zero potential, as well as the $d \propto |\log \Lambda|$ behavior with the vacuum energy $\Lambda$ in the AdS case, as previously proposed in the literature. In the case of large AdS, we also obtain the expected exponent of mass versus distance in a particular scenario, where the mass of the light tower is $m \sim \sqrt{\Lambda}$ and there is a single extra dimension decompactifying. Towards the end of the talk, I discuss the features and shortcomings of alternative but related proposals, as well as future directions. This talk is based on arXiv:2407.02705.