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#### Quantum Gravity from Timelike Liouville theory

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1905.12689.pdf

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Bautista2019_Article_QuantumGravityFromTimelikeLiou.pdf

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##### Citation

Bautista, T., Dabholkar, A., & Erbin, H. (2019). Quantum Gravity from Timelike
Liouville theory.* Journal of High Energy Physics,* *2019*(10):
284. doi:10.1007/JHEP10(2019)284.

Cite as: https://hdl.handle.net/21.11116/0000-0003-CCD2-A

##### Abstract

A proper definition of the path integral of quantum gravity has been a

long-standing puzzle because the Weyl factor of the Euclidean metric has a

wrong-sign kinetic term. We propose a definition of two-dimensional Liouville

quantum gravity with cosmological constant using conformal bootstrap for the

timelike Liouville theory coupled to supercritical matter. We prove a no-ghost

theorem for the states in the BRST cohomology. We show that the four-point

function constructed by gluing the timelike Liouville three-point functions is

well defined and crossing symmetric for external Liouville energies

corresponding to \textit{all} physical states in the BRST cohomology with the

choice of the Ribault--Santachiara contour for the internal energy.

long-standing puzzle because the Weyl factor of the Euclidean metric has a

wrong-sign kinetic term. We propose a definition of two-dimensional Liouville

quantum gravity with cosmological constant using conformal bootstrap for the

timelike Liouville theory coupled to supercritical matter. We prove a no-ghost

theorem for the states in the BRST cohomology. We show that the four-point

function constructed by gluing the timelike Liouville three-point functions is

well defined and crossing symmetric for external Liouville energies

corresponding to \textit{all} physical states in the BRST cohomology with the

choice of the Ribault--Santachiara contour for the internal energy.