Subdivision Analysis of Topological $Z_{p}$ Lattice Gauge Theory
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Date
1993-06-25
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SISSA
Abstract
We analyze the subdivision properties of certain lattice gauge theories for
the discrete abelian groups $Z_{p}$, in four dimensions. In these particular
models we show that the Boltzmann weights are invariant under all $(k,l)$
subdivision moves, when the coupling scale is a $p$th root of unity. For the case of manifolds with boundary, we demonstrate analytically that Alexander type $2$ and $3$ subdivision of a bounding simplex is equivalent to the insertion of an operator which equals a delta function on trivial bounding holonomies. The four dimensional model then gives rise to an effective gauge invariant three dimensional model on its boundary, and we compute the combinatorially invariant value of the partition function for the case of $S^{3}$ and $S^{2}\times S^{1}$.
Description
13 pages, LaTex, ITFA-93-22