Combinatorial Invariants from Four Dimensional Lattice Models

Details Combinatorial Invariants from Four Dimensional Lattice Models Combinatorial Invariants from Four Dimensional Lattice Models

1993-03-19

arxiv.org/abs/hep-th/9303110v1

Int.J.Mod.Phys. A10 (1995) 1329-1342

Physics

High Energy Physics

High Energy Physics - Theory

15 pages

Scientific paper

10.1142/S0217751X95000632

We study the subdivision properties of certain lattice gauge theories based on the groups $Z_{2}$ and $Z_{3}$, in four dimensions. The Boltzmann weights are shown to be invariant under all type $(k,l)$ subdivision moves, at certain discrete values of the coupling parameter. The partition function then provides a combinatorial invariant of the underlying simplicial complex, at least when there is no boundary. We also show how an extra phase factor arises when comparing Boltzmann weights under the Alexander moves, where the boundary undergoes subdivision.

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