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Lattice Gerbe Theory

Lipstein, Arthur E.; Reid-Edwards, Ronald A.

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Ronald A. Reid-Edwards


We formulate the theory of a 2-form gauge field on a Euclidean spacetime lattice. In this approach, the fundamental degrees of freedom live on the faces of the lattice, and the action can be constructed from the sum over Wilson surfaces associated with each fundamental cube of the lattice. If we take the gauge group to be U(1), the theory reduces to the well-known abelian gerbe theory in the continuum limit. We also propose a very simple and natural non-abelian generalization with gauge group U(N)×U(N), which gives rise to U(N) Yang-Mills theory upon dimensional reduction. Formulating the theory on a lattice has several other advantages. In particular, it is possible to compute many observables, such as the expectation value of Wilson surfaces, analytically at strong coupling and numerically for any value of the coupling.


Lipstein, A. E., & Reid-Edwards, R. A. (2014). Lattice Gerbe Theory. Journal of High Energy Physics, 2014(09), Article 034.

Journal Article Type Article
Acceptance Date Aug 14, 2014
Online Publication Date Sep 4, 2014
Publication Date Sep 4, 2014
Deposit Date Feb 22, 2016
Publicly Available Date Jun 14, 2016
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2014
Issue 09
Article Number 034


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Copyright Statement
© The Author(s) 2014 This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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