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 all physical states in the BRST cohomology with the choice of the Ribault-Santachiara contour for the internal energy.

Quantum corrections to finite radius holography and holographic entanglement entropy

“…The simplest solution to the conformal mode problem is simply to rotate the contour to the negative real axis, resulting in a convergent integral [33]. In [34], it was shown how conformal bootstrap can be used to resolve the ambiguities associated to the analytic continuation of the integration over the Weyl mode in two space time dimensions. However, we see here that the contour does not pass through the saddle point at L 0 , so gives a partition function which is exponentially suppressed.…”

Picard-Lefschetz decomposition and Cheshire Cat resurgence in 3D $$ \mathcal{N} $$ = 2 field theories

“…We just need to use b = e iθ with θ ∈ [0, π/2] to connect b = 1 tob = 1. It would be extremely interesting to follow the analytic continuation of the integration contours of the path-integral for Liouville along this path in the complex b plane following the works [27,50].…”

BRST cohomology of timelike Liouville theory

“…Indeed, the factor 1/Q 2 sitting in front of the action in the semi-classical limit can be identified with an appropriate limit of the d-dimensional Newton's constant, which is usually taken as real. The condition Q ∈ R leaves three possible ranges of parameters: spacelike with c L ≥ 25 and Q ≥ 2, spacelike with c L ∈ (1,25) and Q ∈ (0, 2), and timelike with c L ≤ 1 and Q ∈ R. We will focus on these three regimes when discussing applications of this paper. However, reality of the action (or, more generally, any condition on the action) is restrictive since there are interesting theories with a complex Lagrangian or which do not have a Lagrangian at all.…”

“…However, reality of the action (or, more generally, any condition on the action) is restrictive since there are interesting theories with a complex Lagrangian or which do not have a Lagrangian at all. 1 Since Liouville theory is a two-dimensional CFT, it can be completely defined using only CFT techniques. It is within this framework that Liouville theory can be written for Q ∈ C without ambiguities.…”

“…give different spectra. It was proposed in [1] to use BRST quantization as the fundamental guiding principle to determine the spectrum, since it encodes the constraints from the diffeomorphism invariance, the gauge symmetry of gravity.…”