Phase diagram of four-dimensional dynamical triangulations with a boundary

TL;DR

This study explores the phase structure of four-dimensional dynamical triangulations with boundaries, revealing four distinct phases, including a novel three-dimensional phase, with all phase transitions being discontinuous.

Contribution

It provides the first evidence of a three-dimensional phase in 4D dynamical triangulations with boundary conditions, expanding understanding of quantum geometric phases.

Findings

Identified four distinct phases in 4D dynamical triangulations with boundary.

Discovered a phase where the geometry is effectively three-dimensional.

Found all phase transitions to be discontinuous.

Abstract

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.