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arXiv · hep-th/9201036

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

Mordechai Spiegelglas·Shimon Yankielowicz
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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 $G^c_k$, 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 $c\leq 1$ matter systems coupled to two dimensional gravity are pointed out.

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Mordechai Spiegelglas, Shimon Yankielowicz. 1992-01-19. $G/G$--Topological Field Theories by Cosetting $G_k$. https://doi.org/10.1016/0550-3213(93)90247-m

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