Suppression of non-manifold-like sets in the causal set path integral

TL;DR

This paper demonstrates that a Lorentzian path integral with Einstein-Hilbert action can suppress non-manifold-like causal sets, suggesting a natural emergence of manifold-like spacetime structures in quantum gravity.

Contribution

It provides evidence that the path integral framework can inherently favor manifold-like causal sets, advancing understanding of quantum gravity without additional constraints.

Findings

Large class of non-manifold-like sets are suppressed in the path integral

Results support the emergence of manifold-like behavior from quantum causal sets

Proposes a method to generalize suppression to other non-manifold-like classes

Abstract

While it is possible to build causal sets that approximate spacetime manifolds, most causal sets are not at all manifold-like. We show that a Lorentzian path integral with the Einstein-Hilbert action has a phase in which one large class of non-manifold-like causal sets is strongly suppressed, and suggest a direction for generalization to other classes. While we cannot yet show our argument holds for all non-manifold-like sets, our results make it plausible that the path integral might lead to emergent manifold-like behavior with no need for further conditions.