A discretized Chern Simons gauge theory on arbitrary graphs
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Author: Kai Sun, Krishna Kumar, Eduardo Fradkin
Added by: arkiver
Added Date: 2018-06-26
Language: English
Subjects: Strongly Correlated Electrons, High Energy Physics - Theory, Quantum Gases, Condensed Matter
Publishers: arXiv.org
Pages Count: 300
PPI Count: 300
PDF Count: 1
Total Size: 30.96 MB
PDF Size: 9.25 MB
Extensions: pdf, gz, zip, torrent
Contributor: Internet Archive
License: Unknown License
Downloads: 31
Views: 81
Total Files: 12
Media Type: texts
Total Files: 5
Description
In this paper, we show how to discretize the abelian Chern-Simons gauge theory on generic planar lattices/graphs (with or without translational symmetries) embedded in arbitrary 2D closed orientable manifolds. We find that, as long as a one-to-one correspondence between vertices and faces can be defined on the graph such that each face is paired up with a neighboring vertex (and vice versa), a discretized Chern-Simons theory can be constructed consistently. We further verify that all the essential properties of the Chern-Simons gauge theory are preserved in the discretized setup. In addition, we find that the existence of such a one-to-one correspondence is not only a sufficient condition for discretizing a Chern-Simons gauge theory but, for the discretized theory to be nonsingular and to preserve some key properties of the topological field theory, this correspondence is also a necessary one. A specific example will then be provided, in which we discretize the Chern-Simons gauge theory on a tetrahedron.
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