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arXiv · hep-th/9305080

Structure of Topological Lattice Field Theories in Three Dimensions

Stephen-wei Chung·Masafumi Fukuma·Alfred Shapere
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Abstract

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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Stephen-wei Chung, Masafumi Fukuma, Alfred Shapere. 1993-05-19. Structure of Topological Lattice Field Theories in Three Dimensions. https://doi.org/10.1142/s0217751x94000595

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