$G/G$--Topological Field Theories by Cosetting $G_k$

Abstract

$G/G$ topological field theories based on $G_k$ WZW models are constructed and studied. These coset models are formulated as Complex BRST cohomology in $G_k^c$, the complexified level $k$ current algebra. The finite physical spectrum corresponds to the conformal blocks of $G_k$ .The amplitudes for $G/G$ theories are argued to be given in terms of the $G_k$ fusion rules. The $G_k/G_k$ character is the Kac-Weyl numerator of $G_k$ and is interpreted as an index. The Complex BRST cohomology is found to contain states of arbitrary ghost number. Intriguing similarities of $G/G$ to $c\le 1$ matter systems coupled to two dimensional gravity are pointed out.

40 pages (52/2 if use the little option of harvmac.tex)

References in corpus (1)

• Interaction of Discrete States in Two-Dimensional String Theory

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