We report on simulations of DT simplicial gravity for manifolds with the topology of the 4-disk. We find evidence for four phases in a two-dimensional parameter space. In two of these the boundary plays no dynamical role and the geometries are equivalent to those observed earlier for the sphere S^4. In another phase the boundary is maximal and the quantum geometry degenerates to a one dimensional branched polymer. In contrast we provide evidence that the fourth phase is effectively three-dimensional. We find discontinuous phase transitions at all the phase boundaries.
Catterall, Simon and Warner, Simeon, "Phase Diagram of Four-Dimensional Dynamical Triangulations with a Boundary" (2000). Physics. 470.
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