Abstract
We compute the Hermitian sector of the relative BRST cohomology of the spacelike and timelike Liouville theories with generic real central charge cL in each case, coupled to a spacelike Coulomb gas and a generic transverse CFT. This paper is a companion of [1], and its main goal is to completely characterize the cohomology of the timelike theory with cL≤ 1 which was defined there. We also apply our formulas to revisit the BRST cohomology of the spacelike Liouville theory with cL> 1, which includes generalized minimal gravity. We prove a no-ghost theorem for the Hermitian sector in the timelike theory and for some spacelike models.
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