Lattice Topological Field Theory in Two Dimensions

Details Lattice Topological Field Theory in Two Dimensions Lattice Topological Field Theory in Two Dimensions

1992-12-28

arxiv.org/abs/hep-th/9212154v1

Commun. Math. Phys. 161 (1994) 157-176

Physics

High Energy Physics

High Energy Physics - Theory

29 pages (Latex) + 19 figures (uuencoded through uufiles)

Scientific paper

10.1007/BF02099416

The lattice definition of a two-dimensional topological field theory (TFT) is given generically, and the exact solution is obtained explicitly. In particular, the set of all lattice topological field theories is shown to be in one-to-one correspondence with the set of all associative algebras $R$, and the physical Hilbert space is identified with the center $Z(R)$ of the associative algebra $R$. Perturbations of TFT's are also considered in this approach, showing that the form of topological perturbations is automatically determined, and that all TFT's are obtained from one TFT by such perturbations. Several examples are presented, including twisted $N=2$ minimal topological matter and the case where $R$ is a group ring.

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