Related papers: Reduced SL(2,R) WZNW Quantum Mechanics
The reduced SL(2,R) WZW quantum mechanics is analysed in the framework of geometric quantization. The spectrum of the Hamiltonian is determined, and it is found, that contrary to the previous approaches, there is a unique, physically…
Liouville, SL(2,R)/U(1) and SL(2,R)/R_+ coset structures are completely described by gauge invariant Hamiltonian reduction of the SL(2,R) WZNW theory.
The SL(2,R) WZW model, one of the simplest models for strings propagating in curved space time, was believed to be non-unitary in the algebraic treatment involving affine current algebra. It is shown that this was an error that resulted…
Gauged WZNW models are integrable conformal field theories. We integrate the classical \slu{} theory with periodic boundary conditions, which describes closed strings moving in a curved target-space geometry. We calculate its Poisson…
The classification of the coadjoint orbits of the Virasoro algebra is reviewed and is then applied to analyze the so-called global Liouville equation. The review is self-contained, elementary and is tailor-made for the application. It is…
A closed formula for the structure constants in the SL(2,C)/SU(2) WZNW model is derived by a method previously used in Liouville theory. With the help of a reflection amplitude that follows from the structure constants one obtains a…
The origin of the rather mysterious duality symmetry found in quantum Liouville theory is investigated by considering the Liouville theory as the reduction of a WZW-like theory in which the form of the potential for the Cartan field is not…
It is known that Liouville theory can be represented as an SL(2,R) gauged WZW model. We study a two dimensional field theory which can be obtained by analytically continuing some of the variables in the SL(2,R) gauged WZW model. We can…
Many qualitatively new features of WZNW models associated to noncompact cosets are due to zero modes with continuous spectrum. Insight may be gained by reducing the theory to its zero-mode sector, the mini-superspace limit. This will be…
The Schr\"odinger equation is shown to be equivalent to a constrained Liouville equation under the assumption that phase space is extended to Grassmann algebra valued variables. For onedimensional systems, the underlying Hamiltonian…
It is well-known that the Toda Theories can be obtained by reduction from the Wess-Zumino-Novikov-Witten (WZNW) model, but it is less known that this WZNW $\rightarrow$ Toda reduction is \lq incomplete'. The reason for this incompleteness…
Starting with its classical parafermion algebra, we consider the quantisation of the SL(2,R)/U(1) WZNW black hole model.
Using a gauge invariant reduction we directly integrate the SL(2,R)/U(1) WZNW theory. We prove that the conserved parafermions of this theory are coset currents. Quantum mechanically, the parafermion algebra, the energy-momentum tensor, and…
We study the quantum mechanical Liouville model with attractive potential which is obtained by Hamiltonian symmetry reduction from the system of a free particle on $SL(2, \Real)$. The classical reduced system consists of a pair of Liouville…
We study the SL(2,R) WZWN string model describing bosonic string theory in AdS_3 space-time as a deformed oscillator together with its mass spectrum and the string modified SL(2,R) uncertainty relation. The SL(2,R) string oscillator is far…
We investigate the SL(2,R)/U(1) WZW model with level 0<k<2 as a solvable time-dependent background in string theory. This model is expected to be dual to the one describing a rolling closed string tachyon with a time-like linear dilaton. We…
The quantum Wess-Zumino-Witten $\to$ Liouville reduction is formulated using the phase space path integral method of Batalin, Fradkin, and Vilkovisky, adapted to theories on compact two dimensional manifolds. The importance of the zero…
The canonical quantization of the WZNW model provides a complete set of exchange relations in the enlarged chiral state spaces that include the Gauss components of the monodromy matrices. Regarded as new dynamical variables, the elements of…
We consider the gauging of $ SL(2,R) $ WZNW model by its nilpotent subgroup E(1). The resulting space-time of the corresponding sigma model is seen to collapse to a one dimensional field theory of Liouville. Gauging the diagonal subgroup $…
The nonlinear structures in 2D quantum gravity coupled to the $(q+1,q)$ minimal model are studied in the Liouville theory to clarify the factorization and the physical states. It is confirmed that the dressed primary states outside the…