Structure of Topological Lattice Field Theories in Three Dimensions

Details Structure of Topological Lattice Field Theories in Three Dimensions Structure of Topological Lattice Field Theories in Three Dimensions

1993-05-19

arxiv.org/abs/hep-th/9305080v2

Int.J.Mod.Phys. A9 (1994) 1305-1360

Physics

High Energy Physics

High Energy Physics - Theory

63 pages, 46 figures

Scientific paper

10.1142/S0217751X94000595

We construct and classify topological lattice field theories in three dimensions. After defining a general class of local lattice field theories, we impose invariance under arbitrary topology-preserving deformations of the underlying lattice, which are generated by two new local lattice moves. Invariant solutions are in one--to--one correspondence with Hopf algebras satisfying a certain constraint. As an example, we study in detail the topological lattice field theory corresponding to the Hopf algebra based on the group ring $\C[G]$, and show that it is equivalent to lattice gauge theory at zero coupling, and to the Ponzano--Regge theory for $G=$SU(2).

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