Bosonization of ZF algebras: direction toward a deformed Virasoro algebra (original) (raw)

Bosonization of ZF algebras: Direction toward deformed Virasoro algebra

1994

These lectures were prepared to be presented at A.A. Belavin seminar on CFT at Landau Institute for Theoretical Physics. We review bosonization of CFT and show how it can be applied to the studying of representations of Zamolodchikov-Faddeev (ZF) algebras. In the bosonic construction we obtain explicit realization of chiral vertex operators interpolating between irreducible representations of the deformed Virasoro algebra. The commutation relations of these operators are determined by the elliptic matrix of IRF type and their matrix elements are given in the form of the contour integrals of some meromorphic functions. May, 94 †

Generalised bosonic construction of Virasoro algebras

Physics Letters B, 1988

Energy-momentum tensors of conformal field theories and some of their primary fields, including those of parafermionic theories based on simply-laced Lie algebras, are constructed from free bosons. The classification of such theories requires a generalisation of the root systems of Lie algebras. The complete list of such energy-momentum tensors, that can be constructed from lwo free bosons, includes those of the first four c< 1 theories.

Sugawara and Vertex Operator Constructions for Deformed Virasoro Algebras

Annales Henri Poincaré, 2006

From the defining exchange relations of the A q,p (gl N) elliptic quantum algebra, we construct subalgebras which can be characterized as q-deformed W N algebras. The consistency conditions relating the parameters p, q, N and the central charge c are shown to be related to the singularity structure of the functional coefficients defining the exchange relations of specific vertex operators representations of A q,p (gl N) available when N = 2.

Deformed Virasoro Algebras from Elliptic Quantum Algebras

Communications in Mathematical Physics, 2017

We revisit the construction of deformed Virasoro algebras from elliptic quantum algebras of vertex type, generalizing the bilinear trace procedure proposed in the 90's. It allows us to make contact with the vertex operator techniques that were introduced separately at the same period. As a by-product, the method pinpoints two critical values of the central charge for which the center of the algebra is extended, as well as (in the gl(2) case) a Liouville formula.

The Elliptic Scattering Theory of the 1/2-XYZ and Higher Order Deformed Virasoro Algebras

Annales Henri Poincaré, 2006

Bound state excitations of the spin 1/2-XYZ model are considered inside the Bethe Ansatz framework by exploiting the equivalent Non-Linear Integral Equations. Of course, these bound states go to the sine-Gordon breathers in the suitable limit and therefore the scattering factors between them are explicitly computed by inspecting the corresponding Non-Linear Integral Equations. As a consequence, abstracting from the physical model the Zamolodchikov-Faddeev algebra of two n-th elliptic breathers defines a tower of n-order Deformed Virasoro Algebras, reproducing the n = 1 case the usual well-known algebra of Shiraishi-Kubo-Awata-Odake [1].

Bosonization and Vertex Algebras with Defects

Annales Henri Poincaré, 2006

The method of bosonization is extended to the case when a dissipationless point-like defect is present in space-time. Introducing the chiral components of a massless scalar field, interacting with the defect in two dimensions, we construct the associated vertex operators. The main features of the corresponding vertex algebra are established. As an application of this framework we solve the massless Thirring model with defect. We also construct the vertex representation of the sl(2) Kac-Moody algebra, describing the complex interplay between the left and right sectors due to the interaction with the defect. The Sugawara form of the energy-momentum tensor is also explored.

Bosonization of parafermionic conformal field theories

Nuclear Physics B, 1989

We present an explicit construction, in terms of Fubini-Veneziano bosons, of the energy-momentum tensor, parafermionic primary fields and parafermionic operator product algebra for the FateevZamolodchikov-Gepner parafermionic conformal field theories. Other primary fields, including the spin fields and Zk neutral fields, are related to certain momentum states of these bosons. We also show that this bosonization is a special case of a more general construction which associates a Virasoro generator with every (ordered) pair (g, g') of simply-laced algebras.

Realizations of q-Deformed Virasoro Algebra

Progress of Theoretical Physics, 1993

We investigate the q-deformed Virasoro algebra presented by Curtright and Zachos. After showing some new results on the central extension and the operator product expansion, we discuss the relation between the q-deformed Virasoro algebra and the Volterra Poisson bracket algebra. The realization in terms of an infinite set of oscillators is also discussed from the viewpoint of a deformation of the Poisson bracket.