Abstract:
A quantum deformation of 3-dimensional lattice gauge theory is defined by applying the Reshetikhin-Turaev functor to a Heegaard diagram associated to a given cell complex. In the root-of-unity case, the construction is carried out with a modular Hopf algebra. In the topological (weak-coupling) limit, the gauge theory partition function gives a 3-fold invariant, coinciding in the simplicial case with the Turaev-Viro one. We discuss bounded manifolds as well as links in manifolds. By a dimensional reduction, we obtain a q-deformed gauge theory on Riemann surfaces and find a connection with the algebraic Alekseev-Grosse-Schomerus approach.
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Received: 29 April 1996 / Accepted: 24 September 1996
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Boulatov, D. Quantum Deformation of Lattice Gauge Theory . Comm Math Phys 186, 295–322 (1997). https://doi.org/10.1007/s002200050111
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DOI: https://doi.org/10.1007/s002200050111