BRST cohomology of timelike Liouville theory

Abstract

Abstract We compute the Hermitian sector of the relative BRST cohomology of the spacelike and timelike Liouville theories with generic real central charge c L 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 c L ≤ 1 which was defined there. We also apply our formulas to revisit the BRST cohomology of the spacelike Liouville theory with c L > 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.

Keywords

• 2D Gravity
• BRST Quantization
• Models of Quantum Gravity
• Conformal Field Theory