Lattice gerbe theory

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

Abstract

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 explore a very simple and natural non-abelian generalization with gauge group U(N) × U(N). In the classical continuum limit, it reduces to a free theory, but at non-zero lattice spacing it is an interacting theory 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.

Citation

Lipstein, A. E., & Reid-Edwards, R. A. (2014). Lattice gerbe theory. Journal of High Energy Physics, 2014(9), Article ARTN 034. https://doi.org/10.1007/JHEP09%282014%29034

• Journal Article Type: Article
• Acceptance Date: Aug 14, 2014
• Online Publication Date: Sep 4, 2014
• Publication Date: 2014-09
• Deposit Date: Apr 14, 2016
• Publicly Available Date: Apr 14, 2016
• Journal: Journal of high energy physics
• Electronic ISSN: 1029-8479
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 2014
• Issue: 9
• Article Number: ARTN 034
• DOI: https://doi.org/10.1007/JHEP09%282014%29034
• Keywords: Lattice gauge field theories, Gauge symmetry, M-theory, Lattice quantum field theory
• Public URL: https://hull-repository.worktribe.com/output/435997
• Publisher URL: http://link.springer.com/article/10.1007%2FJHEP09(2014)034
• Additional Information: This is a copy of an open access article published in Journal of high energy physics, 2014, v.2014.