Standard and geometric approaches to quantum Liouville theory on the pseudosphere

  title={Standard and geometric approaches to quantum Liouville theory on the pseudosphere},
  author={Pietro Menotti and Erik Tonni},
  journal={Nuclear Physics},

Classical geometry from the quantum Liouville theory

Liouville field theory with heavy charges, I. The pseudosphere

We work out the perturbative expansion of quantum Liouville theory on the pseudosphere starting from the semiclassical limit of a background generated by heavy charges. By solving perturbatively the

Semiclassical limit of the FZZT Liouville theory

Riemann–Hilbert treatment of Liouville theory on the torus

We apply a perturbative technique to study classical Liouville theory on the torus. After mapping the problem on the cut-plane we give the perturbative treatment for a weak source. When the torus

Semiclassical and quantum Liouville theory

We develop a functional integral approach to quantum Liouville field theory completely independent of the hamiltonian approach. To this end on the sphere topology we solve the Riemann-Hilbert problem

On boundary correlators in Liouville theory on AdS2

A bstractWe consider the Liouville theory in fixed Euclidean AdS2 background. Expanded near the minimum of the potential the elementary field has mass squared 2 and (assuming the standard Dirichlet

Liouville field theory with heavy charges. II. The conformal boundary case

We develop a general technique for computing functional integrals with fixed area and boundary length constraints. The correct quantum dimensions for the vertex functions are recovered by properly



Liouville field theory on a pseudosphere

Liouville field theory is considered with boundary conditions corresponding to a quantization of the classical Lobachevskiy plane (i.e. euclidean version of $AdS_2$). We solve the bootstrap equations

Classical and quantal Liouville field theory

The canonical structure of the Liouville theory is investigated. We present two canonical transformations which map the theory onto a free field theory. The first makes use of conformal invariance

Nonperturbative Weak Coupling Analysis of the Liouville Quantum Field Theory

A systematic weak-coupling expansion is developed for the Liouville quantum field theory on a periodic spatial interval. Matrix elements of various Liouville operators are computed to order g/sup 8/

Conformally Invariant Quantization of the Liouville Theory.

The Liouville theory is quantized with use of Fock space methods, an infinite set of charges L/sub n/, n = 0, +- 1,..., is constructed which represents the conformal algebra in two dimensions, and

SO(2,1) Invariant Quantization of the Liouville Theory

The recently proposed SO(2,1)-invariant quantization of the Liouville theory is elaborated. We develop a renormalized perturbation expansion which preserves this symmetry to all orders, but

Correlation functions in Liouville theory.

  • GoulianLi
  • Mathematics, Physics
    Physical review letters
  • 1991
It is shown that after integrating over the zero mode in Liouville correlation functions, the remaining functional integral resembles a free theory and may be evaluated by formally continuing the central charge, and exact agreement is found between theLiouville three-point functions and the results from matrix models.