Timelike boundary and corner terms in the causal set action

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.