Timelike boundary and corner terms in the causal set action

Abstract The causal set action of dimension d is investigated for causal sets that are Poisson sprinklings into manifolds that are regions of d -dimensional Minkowski space. Evidence, both analytic and numerical, is provided for the conjecture that as the discreteness length l tends to zero, the mean of the causal set action over Poisson sprinklings into a manifold with a timelike boundary, is dominated by a term proportional to the volume of the timelike boundary and diverges like l −1 . A novel conjecture for the contribution to the causal set action from co-dimension two corners, also known as joints, is proposed and justified.