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 (numerically) 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.

42 pages

References in corpus (44)

• Structure Constants and Conformal Bootstrap in Liouville Field Theory
• Introduction to string field theory
• Closed String Field Theory: Quantum Action and the BV Master Equation
• Two and three-point functions in Liouville theory
• Liouville theory revisited
• Liouville Field Theory -- A decade after the revolution
• Analytic Continuation of Liouville Theory
• On the Liouville three-point function
• Rolling Tachyons from Liouville theory
• A lecture on the Liouville vertex operators
• BRST Analysis of Physical States for 2D (Super) Gravity Coupled to (Super) Conformal Matter
• Quantum black holes, localization and the topological string
• Cutkosky Rules for Superstring Field Theory
• Closed Superstring Field Theory and its Applications
• Liouville theory with a central charge less than one
• A non-rational CFT with c=1 as a limit of minimal models
• Localization in Supergravity and Quantum $Ad{S}_4/CF{T}_3$ Holography
• Three-point functions in c <= 1 Liouville theory and conformal loop ensembles
• Bulk correlation functions in 2D quantum gravity
• Closed String Tachyon Condensation and Worldsheet Inflation
• Boundary Liouville Theory and 2D Quantum Gravity
• Unitarity of Superstring Field Theory
• Modular bootstrap in Liouville field theory
• Notes on Liouville Theory at c<=1
• Non-Rational 2D Quantum Gravity: I. World Sheet CFT
• On Minisuperspace Models of S-branes
• Unitarity of the Box Diagram
• On the timelike Liouville three-point function
• Analyticity and Crossing Symmetry of Superstring Loop Amplitudes
• Modeling Quantum Gravity Effects in Inflation
• Quantum mechanical Liouville model with attractive potential
• Non-Rational 2D Quantum Gravity II. Target Space CFT
• Reduced SL(2,R) WZNW Quantum Mechanics
• Liouville theory without an action
• Remarks on the BRST-cohomology for $c_M>1$ matter coupled to ``Liouville gravity"
• Quantum Cosmology Near Two Dimensions
• Liouville field theory and log-correlated Random Energy Models
• Quantum Weyl Invariance and Cosmology
• Equivalence of Two Contour Prescriptions in Superstring Perturbation Theory
• Matrix Model and Time-like Linear Dilaton Matter
• The no-ghost theorem for string theory in curved backgrounds with a flat timelike direction
• Gauge Invariant Computable Quantities In Timelike Liouville Theory
• Operator Product Expansion in Liouville Field Theory and Seiberg type transitions in log-correlated Random Energy Models
• Analytic continuation of 3-point functions of the conformal field theory

Cited by in corpus (15)

• Solving 3d Gravity with Virasoro TQFT
• The Virasoro Minimal String
• Finite Features of Quantum De Sitter Space
• Quantum corrections to finite radius holography and holographic entanglement entropy
• Picard-Lefschetz decomposition and Cheshire Cat resurgence in 3D $\mathcal{N}=2$ field theories
• Comments on the Quantum Field Theory of the Coulomb Gas Formalism
• The complex Liouville string: the worldsheet
• A Two-Dimensional String Cosmology
• The Torus One-Point Diagram in Two-Dimensional String Cosmology
• 2D quantum gravity partition function on the fluctuating sphere
• BRST cohomology of timelike Liouville theory
• The two-sphere partition function in two-dimensional quantum gravity
• Gravitational action for a massive Majorana fermion in 2d quantum gravity
• The two-sphere partition function from timelike Liouville theory at three-loop order
• Probabilistic construction of non compactified imaginary Liouville field theory