Timelike boundary and corner terms in the causal set action

TL;DR

This paper investigates the causal set action in Minkowski space with timelike boundaries, proposing a divergence behavior and a new conjecture for corner contributions, supported by analytic and numerical evidence.

Contribution

It introduces a novel conjecture for the contribution of co-dimension 2 corners to the causal set action and analyzes divergence behavior near timelike boundaries.

Findings

Mean causal set action diverges as l^{-1} near timelike boundaries

Proposes a new conjecture for corner (joint) contributions to the action

Provides analytic and numerical evidence supporting the conjecture

Abstract

The causal set action of dimension $d$ is investigated for causal sets that are Poisson sprinklings into submanifolds of $d$-dimensional Minkowski space. Evidence, both analytic and numerical, is provided for the conjecture that the mean of the causal set action over sprinklings into a manifold with a timelike boundary, diverges like $l^{-1}$ in the continuum limit as the discreteness length $l$ tends to zero. A novel conjecture for the contribution to the causal set action from co-dimension 2 corners, also known as joints, is proposed and justified.