# Standard and geometric approaches to quantum Liouville theory on the pseudosphere

@article{Menotti2005StandardAG, title={Standard and geometric approaches to quantum Liouville theory on the pseudosphere}, author={Pietro Menotti and Erik Tonni}, journal={Nuclear Physics}, year={2005}, volume={707}, pages={321-346} }

## 18 Citations

### Liouville field theory with heavy charges, I. The pseudosphere

- Physics, Mathematics
- 2006

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…

### Riemann–Hilbert treatment of Liouville theory on the torus

- Mathematics
- 2011

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

- Mathematics, Physics
- 2005

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

- MathematicsJournal of High Energy Physics
- 2019

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

- Mathematics
- 2006

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…

## References

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- Mathematics
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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

- Mathematics
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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

- Physics, Mathematics
- 1983

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/…

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- Mathematics
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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

- Mathematics
- 1983

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.

- Mathematics, PhysicsPhysical 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.