English

Lattice Topological Field Theory in Two Dimensions

High Energy Physics - Theory 2009-10-22 v1

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 RR, and the physical Hilbert space is identified with the center Z(R)Z(R) of the associative algebra RR. 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=2N=2 minimal topological matter and the case where RR is a group ring.

Keywords

Cite

@article{arxiv.hep-th/9212154,
  title  = {Lattice Topological Field Theory in Two Dimensions},
  author = {M. Fukuma and S. Hosono and H. Kawai},
  journal= {arXiv preprint arXiv:hep-th/9212154},
  year   = {2009}
}

Comments

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

R2 v1 2026-07-22T15:44:41.991Z