Evidence for the continuum in 2D causal set quantum gravity

Abstract

We present evidence for a continuum phase in a theory of 2D causal set quantum gravity which contains a dimensionless non-locality parameter epsilon ∈ (0, 1]. We also find a phase transition between this continuum phase and a new crystalline phase which is characterized by a set of covariant observables. For a fixed size of the causal set, the transition temperature β−1c decreases monotonically with epsilon. The locus of the transition in the β2 versus epsilon plane asymptotically approaches to the infinite temperature axis, suggesting that the continuum phase survives the analytic continuation.