Lukyanov's screening operators for the deformed Virasoro algebra

doi:10.1016/S0375-9601(97)00200-4

Physics Letters A

Volume 229, Issue 5, 26 May 1997, Pages 285-292

https://doi.org/10.1016/S0375-9601(97)00200-4 Get rights and content

Abstract

The BRST property of Lukyanov's screening operators in the bosonic representation of the deformed virasoro algebra is proven.

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We continue the study of form factors of descendant operators in the sinh- and sine-Gordon models in the framework of the algebraic construction proposed in [1]. We find the algebraic construction to be related to a particular limit of the tensor product of the deformed Virasoro algebra and a suitably chosen Heisenberg algebra. To analyze the space of local operators in the framework of the form factor formalism we introduce screening operators and construct singular and cosingular vectors in the Fock spaces related to the free field realization of the obtained algebra. We show that the singular vectors are expressed in terms of the degenerate Macdonald polynomials with rectangular partitions. We study the matrix elements that contain a singular vector in one chirality and a cosingular vector in the other chirality and find them to lead to the resonance identities already known in the conformal perturbation theory. Besides, we give a new derivation of the equation of motion in the sinh-Gordon theory, and a new representation for conserved currents.
Free field construction for the eight-vertex model: Representation for form factors
2002, Nuclear Physics B
The free field realization of the eight-vertex model is extended to form factors. It is achieved by constructing off-diagonal with respect to the ground state sectors matrix elements of the Λ operator which establishes a relation between corner transfer matrices of the eight-vertex model and of the SOS model. As an example, the two-particle form factor of the σ^z operator is evaluated explicitly.
Hidden Virasoro symmetry of (soliton solutions of) the sine-Gordon theory
2000, Nuclear Physics B
We present a construction of a Virasoro symmetry of the sine-Gordon (SG) theory. It is a dynamical one and has nothing to do with the space–time Virasoro symmetry of 2D CFT. Although it is clear how it can be realized directly in the SG field theory, we are rather concerned here with the corresponding N-soliton solutions. We present explicit expressions for their infinitesimal transformations and show that they are local in this case. Some preliminary stages about the quantization of the classical results presented in this paper are also given.
Free field construction for correlation functions of the eight-vertex model
1998, Nuclear Physics B
A free field representation for the type I vertex operators and the corner transfer matrices of the eight-vertex model is proposed. The construction uses the vertex-face correspondence, which makes it possible to express correlation functions of the eight-vertex model in terms of correlation functions of the SOS model with a non-local insertion. This new non-local insertion admits a free field representation in terms of Lukyanov's screening operator. The spectrum of the corner transfer matrix and the Baxter-Kelland formula for the average staggered polarization have been reproduced.
Generalized Macdonald Functions on Fock Tensor Spaces and Duality Formula for Changing Preferred Direction
2020, Communications in Mathematical Physics
Lattice models, deformed Virasoro algebra and reduction equation
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Lukyanov's screening operators for the deformed Virasoro algebra

Abstract

Phys. Lett. A

Phys. Lett. B

Nucl. Phys. B

Nucl. Phys. B

Comm. Math. Phys.