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Lattice Topological Field Theory in Two Dimensions

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arxiv hep-th/9212154 v1 pith:5L6JNSQC submitted 1992-12-28 hep-th

classification hep-th
keywords topologicalfieldlatticeperturbationsassociativeobtainedtheoryalgebra
verification ladder T0 review T1 audit T2 compute T3 formal

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abstract

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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Cited by 2 Pith papers

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