Towards a dual spin network basis for (3+1)d lattice gauge theories and topological phases View Full Text


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Article Info

DATE

2018-10

AUTHORS

Clement Delcamp, Bianca Dittrich

ABSTRACT

Using a recent strategy to encode the space of flat connections on a three-manifold with string-like defects into the space of flat connections on a so-called 2d Heegaard surface, we propose a novel way to define gauge invariant bases for (3+1)d lattice gauge theories and gauge models of topological phases. In particular, this method reconstructs the spin network basis and yields a novel dual spin network basis. While the spin network basis allows to interpret states in terms of electric excitations, on top of a vacuum sharply peaked on a vanishing electric field, the dual spin network basis describes magnetic (or curvature) excitations, on top of a vacuum sharply peaked on a vanishing magnetic field (or flat connection). This technique is also applicable for manifolds with boundaries. We distinguish in particular a dual pair of boundary conditions, namely of electric type and of magnetic type. This can be used to consider a generalization of Ocneanu’s tube algebra in order to reveal the algebraic structure of the excitations associated with certain 3d manifolds. More... »

PAGES

23

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/jhep10(2018)023

DOI

http://dx.doi.org/10.1007/jhep10(2018)023

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1107431153


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