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

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.

14 pages, 10 figures. Section 2 revised and more figures added. Some editing in the introduction and conclusion section, section 3.1 renamed and references added