相关论文: Quantum Exchange Algebra and Exact Operator Soluti…

Quantum $A_2$-Toda field theory in two dimensions is investigated based on the method of quantizing canonical free field. Toda exponential operators associated with the fundamental weights are constructed to the fourth order in the…

Quantum $A_N$-Toda field theory in two dimensions is investigated based on the method of quantizing canonical free field. Toda exponential operator associated with the fundamental weight $\lambda^1$ is constructed.

Exact operator solution for quantum Liouville theory is investigated based on the canonical free field. Locality, the field equation and the canonical commutation relations are examined based on the exchange algebra hidden in the theory.…

We study the Toda field theory with finite Lie algebras using an extension of the Goulian-Li technique. In this way, we show that, after integrating over the zero mode in the correlation functions of the exponential fields, the resulting…

Using the reduced WZNW formulation we analyse the classical $W$ orbit content of the space of classical solutions of the $A_2$ Toda theory. We define the quantized Toda field as a periodic primary field of the $W$ algebra satisfying the…

We provide explicit realizations for the operators which when exchanged give rise to the scattering matrix. For affine Toda field theory we present two alternative constructions, one related to a free bosonic theory and the other formally…

A class of two-dimensional field theories with exponential interactions is introduced. The interaction depends on two ``coupling'' matrices and is sufficiently general to include all Toda field theories existing in the literature. Lie point…

We study the Liouville theory on a Riemann surface of genus g by means of their associated Drinfeld--Sokolov linear systems. We discuss the cohomological properties of the monodromies of these systems. We identify the space of solutions of…

We consider the $C_2$ Toda theory in the reduced WZNW framework. Analysing the classical representation space of the symmetry algebra (which is the corresponding $C_2$ $W$ algebra) we determine its classical highest weight representations.…

We derive an explicit, exactly conformally invariant form for the action for the non-abelian Toda field theory. We demonstrate that the conformal invariance conditions, expressed in terms of the $\beta$-functions of the theory, are…

Liouville and Toda gravity theories with non-vanishing interaction potentials have spectra obtained by dividing the free-field spectra for these cases by the Weyl group of the corresponding $A_1$ or $A_2$ Lie algebra. We study the canonical…

Vertex operators are constructed providing representations of the exchange relations containing either the S-matrix of a real coupling (simply-laced) affine Toda field theory, or its minimal counterpart. One feature of the construction is…

This paper investigates the relations between the Toda conformal field theories, quantum group theory and the quantisation of moduli spaces of flat connections. We use the free field representation of the $\mathcal{W}$-algebras to define…

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…

We provide a proposal, motivated by Separation of Variables and gauge theory arguments, for constructing exact solutions to the quantum Baxter equation associated to the $N$-particle relativistic Toda chain and test our proposal against…

The properties of completely degenerate fields in the Conformal Toda Field Theory are studied. It is shown that a generic four-point correlation function that contains only one such field does not satisfy ordinary differential equation in…

In this paper we introduce a class of generalized supersymmetric Toda field theories. The theories are labeled by a continuous parameter and have $N=2$ supersymmetry. They include previously known $N=2$ Toda theories as special cases. Using…

We quantize $sl_n$ Toda field theories in a periodic lattice. We find the quantum exchange algebra in the diagonal monodromy (Bloch wave) basis in the case of the defining representation. In the $sl_3$ case we extend the analysis also to…

A detailed reexamination is made of the exact operator formalism of two-dimensional Liouville quantum gravity in Minkowski spacetime with the cosmological term fully taken into account. Making use of the canonical mapping from the…

Generalizations of GL(n) abelian Toda and $\widetilde{GL}(n)$ abelian affine Toda field theories to the noncommutative plane are constructed. Our proposal relies on the noncommutative extension of a zero-curvature condition satisfied by…