English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this paper, we show how to discretize the abelian Chern-Simons gaugetheory on generic planar lattices/graphs (with or without translationalsymmetries) embedded in arbitrary 2D closed orientable manifolds. We find that,as long as a one-to-one correspondence between vertices and faces can bedefined on the graph such that each face is paired up with a neighboring vertex(and vice versa), a discretized Chern-Simons theory can be constructedconsistently. We further verify that all the essential properties of theChern-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 asufficient condition for discretizing a Chern-Simons gauge theory but, for thediscretized theory to be nonsingular and to preserve some key properties of thetopological field theory, this correspondence is also a necessary one. Aspecific example will then be provided, in which we discretize the Chern-Simonsgauge theory on a tetrahedron.

A discretized Chern-Simons gauge theory on arbitrary graphs