Quantum Deformation of Lattice Gauge Theory

Details Quantum Deformation of Lattice Gauge Theory Quantum Deformation of Lattice Gauge Theory

1996-04-19

arxiv.org/abs/hep-th/9604117v1

Commun.Math.Phys. 186 (1997) 295-322

Physics

High Energy Physics

High Energy Physics - Theory

31 pp.; uses epic.sty and eepic.sty

Scientific paper

10.1007/s002200050111

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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