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BRST cohomology of timelike Liouville theory

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Bautista,  Teresa
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Citation

Bautista, T., Erbin, H., & Kudrna, M. (2020). BRST cohomology of timelike Liouville theory. Journal of High Energy Physics, 2020(5): 29. doi:10.1007/JHEP05(2020)029.


Cite as: https://hdl.handle.net/21.11116/0000-0005-A68F-F
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 arXiv:1905.12689, and its main goal is to
completely characterize the cohomology of the timelike theory with $c_L < 1$
which was there defined. 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.