A Lecture on the Liouville Vertex Operators
نویسنده
چکیده
We reconsider the construction of exponential fields in the quantized Liouville theory. It is based on a free-field construction of a continuous family or chiral vertex operators. We derive the fusion and braid relations of the chiral vertex operators. This allows us to simplify the verification of locality and crossing symmetry of the exponential fields considerably. The calculation of the matrix elements of the exponential fields leads to a constructive derivation of the formula proposed by Dorn/Otto and the brothers Zamolodchikov.
منابع مشابه
De Sitter Gravity and Liouville Theory
We show that the spectrum of conical defects in three-dimensional de Sitter space is in one-toone correspondence with the spectrum of vertex operators in Liouville conformal field theory. The classical conformal dimensions of vertex operators are equal to the masses of the classical point particles in dS3, that cause the conical defect. The quantum dimensions instead are shown to coincide with ...
متن کاملLiouville theory without an action
We show that the conformal bootstrap allows to solve the Liouville conformal field theory without any perturbative computation. In particular, the bootstrap provides the special structure constants that were previously computed perturbatively, up to rescalings of the vertex operators. We also show that there are constraints on the allowed normalization and rescalings of the vertex operators. ar...
متن کاملInverse spectral problems for Sturm-Liouville operators with transmission conditions
Abstract: This paper deals with the boundary value problem involving the differential equation -y''+q(x)y=lambda y subject to the standard boundary conditions along with the following discontinuity conditions at a point y(a+0)=a1y(a-0), y'(a+0)=a2y'(a-0)+a3y(a-0). We develop the Hochestadt-Lieberman’s result for Sturm-Lio...
متن کاملEigenfunction expansion in the singular case for q-Sturm-Liouville operators
In this work, we prove the existence of a spectral function for singular q-Sturm-Liouville operator. Further, we establish a Parseval equality and expansion formula in eigenfunctions by terms of the spectral function.
متن کاملA Note on Quantum Liouville Theory via Quantum Group ——- An Approach to Strong Coupling Liouville Theory ——-
Quantum Liouville theory is annualized in terms of the infinite dimensional representations of Uqsl(2,C) with q a root of unity. Making full use of characteristic features of the representations, we show that vertex operators in this Liouville theory are factorized into classical vertex operators and those which are constructed from the finite dimensional representations of Uqsl(2,C). We furthe...
متن کامل