Physical States in G/G Models and 2d Gravity

Abstract

An analysis of the BRST cohomology of the G/G topological models is performed for the case of $A_1^{(1)}$. Invoking a special free field parametrization of the various currents, the cohomology on the corresponding Fock space is extracted. We employ the singular vector structure and fusion rules to translate the latter into the cohomology on the space of irreducible representations. Using the physical states we calculate the characters and partition function, and verify the index interpretation. We twist the energy-momentum tensor to establish an intriguing correspondence between the $\frac{SL(2)}{SL(2)}$ model with level $k=\frac{p}{q}-2$ and $(p,q)$ models coupled to gravity.

42 pages

References in corpus (3)

• $G/G$--Topological Field Theories by Cosetting $G_k$
• Topological Matter, Integrable Models and Fusion Rings
• Discrete States of 2D String Theory in Polyakov's Light-Cone Gauge

Cited by in corpus (33)

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