Conserved Topological Defects in Non-Embedded Graphs in Quantum Gravity

Details Conserved Topological Defects in Non-Embedded Graphs in Quantum Gravity Conserved Topological Defects in Non-Embedded Graphs in Quantum Gravity

2008-05-20

arxiv.org/abs/0805.3175v2

Class.Quant.Grav.25:205015,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

42 pages, 34 figures

Scientific paper

10.1088/0264-9381/25/20/205015

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.

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