Quantum Gravity from Timelike Liouville theory

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.
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https://hal.archives-ouvertes.fr/hal-02160627
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Submitted on : Wednesday, June 19, 2019 - 7:47:36 PM
Last modification on : Wednesday, August 14, 2019 - 10:50:12 PM

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Teresa Bautista, Atish Dabholkar, Harold Erbin. Quantum Gravity from Timelike Liouville theory. 2019. ⟨hal-02160627⟩

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