Boundary Terms for Causal Sets

TL;DR

This paper introduces boundary terms for causal set actions that recover known continuum boundary terms and relate to geometric volumes in flat spacetime, advancing causal set quantum gravity.

Contribution

It proposes a new family of boundary terms for causal sets and demonstrates their continuum limit matches the Gibbons-Hawking-York term and relates to geometric volumes.

Findings

Boundary terms recover Gibbons-Hawking-York in the continuum limit

Mean causal set action relates to volume of intersection of light-cone boundaries

Results connect causal set actions with continuum geometric quantities

Abstract

We propose a family of boundary terms for the action of a causal set with a spacelike boundary. We show that in the continuum limit one recovers the Gibbons-Hawking-York boundary term in the mean. We also calculate the continuum limit of the mean causal set action for an Alexandrov interval in flat spacetime. We find that it is equal to the volume of the codimension-2 intersection of the two light-cone boundaries of the interval.