Conserved Topological Defects in Non-Embedded Graphs in Quantum Gravity

Abstract

We follow up on previous work which found that commonly used graph evolution moves lead to conserved quantities that can be expressed in terms of the braiding of the graph in its embedding space. We study non-embedded graphs under three distinct sets of dynamical rules and find non-trivial conserved quantities that can be expressed in terms of topological defects in the dual geometry. For graphs dual to 2-dimensional simplicial complexes we identify all the conserved quantities of the evolution. We also indicate expected results for graphs dual to 3-dimensional simplicial complexes.