Correlation functions and vertex operators of Liouville theory

Jorjadze, George; Weigt, G.

doi:10.1016/j.physletb.2003.11.067

Cited by 14 publications

(16 citation statements)

References 20 publications

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“…For normalizable states with α = Q 2 + iR, the last expression is consistent with the anomalous hermiticity of p, 24) which follows from the presence of the background charge. In order to define the quantum version of e − bϕ 2 , let us define the "screening charges"…”

Section: The Reflection Coefficient and The Liouville Dualitysupporting

confidence: 65%

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FZZ Scattering

Pakman

2006

J. High Energy Phys.

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Abstract:We study the duality between the two dimensional black hole and the sine-Liouville conformal field theories via exact operator quantization of a classical scattering problem. The ideas are first illustrated in Liouville theory, which is dual to itself under the interchange of the Liouville parameter b by 1/b. In both cases, a classical scattering problem does not determine uniquely the quantum reflection coefficient. The latter is only fixed by assuming that the dual scattering problem has the same reflection coefficient. We also discuss the relation of this approach with the method that exploits the parafermionic symmetry of the model to compute the reflection coefficient.

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Section: The Reflection Coefficient and The Liouville Dualitysupporting

confidence: 65%

“…Therefore it is natural to try to quantize Liouville theory by quantizing the mapping to this free field via operator quantization. This program has been carried out successfully in [21] were the DOZZ formula [22,23] for the Liouville three point function was reobtained (see also [24]). …”

Section: Duality In Liouville Scatteringmentioning

confidence: 99%

FZZ Scattering

Pakman

2006

J. High Energy Phys.

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“…But for α = − n 2 the series becomes finite, as it is expected from the classical picture. V − n 2 contains only n + 1 terms and one can obtain the corresponding correlation function p ′ , 0|V − n 2 |p, 0 in a closed form [14]. The continuation of this expression to arbitrary α reproduces the 3-point correlation function of [11,12].…”

Section: Some Open Problems Of the Operator Approach To Bltmentioning

confidence: 91%

Operator approach to boundary Liouville theory

Dorn

Jorjadze

2008

Annals of Physics

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We propose new methods for calculation of the discrete spectrum, the reflection amplitude and the correlation functions of boundary Liouville theory on a strip with Lorentzian signature. They are based on the structure of the vertex operator V = e −ϕ in terms of the asymptotic operators. The methods first are tested for the particle dynamics in the Morse potential, where similar structures appear. Application of our methods to boundary Liouville theory reproduces the known results obtained earlier in the bootstrap approach, but there can arise a certain extension when the boundary parameters are near to critical values. Namely, in this case we have found up to four different equidistant series of discrete spectra, and the reflection amplitude is modified respectively.

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“…Equation (2.13) is invariant under the SL(2, R) transformations Ψ → SΨ. The corresponding infinitesimal form of ξ(x) is 17) and for ξ(x) = x it is constant T = − 18) and it is associated with the vacuum of the system. The vacuum solution is invariant under the SL(2, R) subgroup of conformal transformations generated by the vector fields ∂ x , cos x∂ x and sin x∂ x and this symmetry is a particular case of (2.16) for ξ(x) = x.…”

Section: Dirichlet Conditionmentioning

confidence: 99%

Boundary Liouville Theory: Hamiltonian Description and Quantization

Dorn

Jorjadze²

2007

SIGMA

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Abstract. The paper is devoted to the Hamiltonian treatment of classical and quantum properties of Liouville field theory on a timelike strip in 2d Minkowski space. We give a complete description of classical solutions regular in the interior of the strip and obeying constant conformally invariant conditions on both boundaries. Depending on the values of the two boundary parameters these solutions may have different monodromy properties and are related to bound or scattering states. By Bohr-Sommerfeld quantization we find the quasiclassical discrete energy spectrum for the bound states in agreement with the corresponding limit of spectral data obtained previously by conformal bootstrap methods in Euclidean space. The full quantum version of the special vertex operator e −ϕ in terms of free field exponentials is constructed in the hyperbolic sector.

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Correlation functions and vertex operators of Liouville theory

Cited by 14 publications

References 20 publications

FZZ Scattering

FZZ Scattering

Operator approach to boundary Liouville theory

Boundary Liouville Theory: Hamiltonian Description and Quantization

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