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Lattice topological field theory in two dimensions

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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 algebrasR, and the physical Hilbert space is identified with the centerZ(R) of the associative algebraR. 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 twistedN=2 minimal topological matter and the case whereR is a group ring.

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Author notes

  1. S. Hosono

    Present address: Dept. of Math., Toyama Univ., 930, Toyama, Japan

Authors and Affiliations

  1. Laboratory of Nuclear Studies, Cornell University, 14853, Ithaea, NY, USA

    M. Fukuma

  2. Department of Mathematics, Harvard University, 02138, Cambridge, MA, USA

    S. Hosono

  3. Department of Physics, University of Tokyo, Hongo, 113, Tokyo, Japan

    H. Kawai

Authors
  1. M. Fukuma
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  2. S. Hosono
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  3. H. Kawai
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Communicated by S.-T. Yau

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Fukuma, M., Hosono, S. & Kawai, H. Lattice topological field theory in two dimensions. Commun.Math. Phys. 161, 157–175 (1994). https://doi.org/10.1007/BF02099416

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  • DOI: https://doi.org/10.1007/BF02099416

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