Classification and construction of unitary topological field theories in two dimensions

Details Classification and construction of unitary topological field theories in two dimensions Classification and construction of unitary topological field theories in two dimensions

1993-08-09

arxiv.org/abs/hep-th/9308043v1

J.Math.Phys. 35 (1994) 5306-5313

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, latex

Scientific paper

10.1063/1.530752

We prove that unitary two-dimensional topological field theories are uniquely characterized by $n$ positive real numbers $\lambda _1,\ldots \lambda _n$ which can be regarded as the eigenvalues of a hermitean handle creation operator. The number $n$ is the dimension of the Hilbert space associated with the circle and the partition functions for closed surfaces have the form $$ Z_g=\sum_{i=1}^{n}\lambda _i^{g-1} $$ where $g$ is the genus. The eigenvalues can be arbitary positive numbers. We show how such a theory can be constructed on triangulated surfaces.

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