Topology and Duality in Abelian Lattice Theories
Abstract
We show how to obtain the dual of any lattice model with inhomogeneous local interactions based on an arbitrary Abelian group in any dimension and on lattices with arbitrary topology. It is shown that in general the dual theory contains disorder loops on the generators of the cohomology group of a particular dimension. An explicit construction for altering the statistical sum to obtain a self-dual theory, when these obstructions exist, is also given. We discuss some applications of these results, particularly the existence of non-trivial self-dual 2-dimensional Z_N theories on the torus. In addition we explicitly construct the n-point functions of plaquette variables for the U(1) gauge theory on the 2-dimensional g-tori.
Cite
@article{arxiv.hep-th/9712173,
title = {Topology and Duality in Abelian Lattice Theories},
author = {C. R. Gattringer and S. Jaimungal and G. W. Semenoff},
journal= {arXiv preprint arXiv:hep-th/9712173},
year = {2008}
}
Comments
11 pages, LateX, 1 epsf figure; minor typos corrected and references updated