Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1992-12-28
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.
Fukuma Masafumi
Hosono Shinobu
Kawai Hajime
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