Classification and construction of unitary topological field theories in two dimensions

Abstract

We prove that unitary two-dimensional topological field theories are uniquely characterized by $n$ positive real numbers ${\lambda }_1,\dots {\lambda }_n$ 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.

12 pages, latex

References in corpus (1)

• Topological Models on the Lattice and a Remark on String Theory Cloning

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