Entropy and the Link Action in the Causal Set Path-Sum

TL;DR

This paper investigates how the link action influences the suppression of dominant non-manifold-like causal sets in the causal set path-sum, contributing to the understanding of quantum gravity models.

Contribution

It extends previous work by analyzing the effect of the link action on sub-dominant orders, showing it suppresses dominant orders in the causal set path-sum.

Findings

Link action suppresses Kleitman-Rothschild orders

Extension of Loomis and Carlip's work on sub-dominant orders

Dominance of non-manifold-like orders is mitigated by the link action

Abstract

In causal set theory the gravitational path integral is replaced by a path-sum over a sample space $\Omega_n$ of $n$-element causal sets. The contribution from non-manifold-like orders dominates $\Omega_n$ for large $n$ and therefore must be tamed by a suitable action in the low energy limit of the theory. We extend the work of Loomis and Carlip on the contribution of sub-dominant bilayer orders to the causal set path-sum and show that the "link action" suppresses the dominant Kleitman-Rothschild orders for the same range of parameters.