Numerical Evaluation of the Causal Set Propagator in 2D Anti-de Sitter Spacetime

Abstract

We numerically investigate the application of the path-sum-based causal set scalar propagator construction to (1+1)-dimensional Anti-de Sitter (AdS) spacetime. Building upon a generalization of Johnston's path sum approach, we simulate Poisson-sprinkled causal sets in AdS$_{1+1}$ and numerically evaluate the retarded scalar propagator, comparing it to the known continuum result. Our results confirm that even in curved spacetimes with constant negative curvature, the discrete causal set path sum reproduces the continuum propagator without modification of the flat-spacetime jump amplitudes, thereby providing further numerical support for former analytical results and the applicability of the path sum formalism to curved Lorentzian manifolds.