Canonical equivalence of Liouville and free fields

Ford, C. J. B.; Sachs, Ivo

doi:10.1016/s0370-2693(97)01510-4

Cited by 5 publications

(6 citation statements)

References 8 publications

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“…The problem of computing correlation functions of arbitrary vertex operators in the Liouville theory then reduces to the problem of computing a double infinite series of correlation functions of powers of integrated vertex operators in a free scalar theory. This is reminiscent of the classical equivalence of the Liouville theory and the free theory by a canonical transformation [9]. However, this is a little too restrictive because the zero mode integration then forces certain combinations of the parameters to be positive integers.…”

Section: Path Integration Symmetries and Renormalisationmentioning

confidence: 98%

Duality in Quantum Liouville Theory

O’Raifeartaigh¹,

Pawlowski²,

Sreedhar³

1999

Annals of Physics

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The quantisation of the two-dimensional Liouville field theory is investigated using the path integral, on the sphere, in the large radius limit. The general form of the N -point functions of vertex operators is found and the three-point function is derived explicitly. In previous work it was inferred that the three-point function should possess a two-dimensional lattice of poles in the parameter space (as opposed to a one-dimensional lattice one would expect from the standard Liouville potential). Here we argue that the two-dimensionality of the lattice has its origin in the duality of the quantum mechanical Liouville states and we incorporate this duality into the path integral by using a two-exponential potential. Contrary to what one might expect, this does not violate conformal invariance; and has the great advantage of producing the two-dimensional lattice in a natural way.

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Section: Path Integration Symmetries and Renormalisationmentioning

confidence: 98%

Duality in Quantum Liouville Theory

O’Raifeartaigh¹,

Pawlowski²,

Sreedhar³

1999

Annals of Physics

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“…It might be interesting to notice here that the investigations initiated by the references [4,5] are based on Liouville's second form of the general solution [1]. This approach led [4] to a parametrisation of the Liouville theory in terms of a canonically related [19] but pseudo-scalar free field which is asymptotically neither an in-nor an out-field, whereas the work of [5,10] mainly treats the singular elliptic monodromy for which we do not know whether there exists a parametrisation in terms of a real free field at all.…”

Section: Free-field Parametrisationmentioning

confidence: 99%

Correlation functions and vertex operators of Liouville theory

Jorjadze¹,

Weigt

2004

Physics Letters B

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We calculate correlation functions for vertex operators with negative integer exponentials of a periodic Liouville field, and derive the general case by continuing them as distributions. The path-integral based conjectures of Dorn and Otto prove to be conditionally valid only. We formulate integral representations for the generic vertex operators and indicate structures which are related to the Liouville S-matrix.

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“…and (3.16). The 2-dim σ-model corresponding to the metric (3.11)11 A generating functional of the type(3.27), containing first derivatives of the fields in a nonpolynomial way, has appeared in a study on the canonical equivalence between Liouville and free field theories[32] (also[33] as quoted in[32]).…”

mentioning

confidence: 99%

Duality-invariant class of two-dimensional field theories

Sfetsos

1999

Nuclear Physics B

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We construct a new class of two-dimensional field theories with target spaces that are finite multiparameter deformations of the usual coset G/H-spaces. They arise naturally, when certain models, related by Poisson-Lie T-duality, develop a local gauge invariance at specific points of their classical moduli space. We show that canonical equivalences in this context can be formulated in loop space in terms of parafermionic-type algebras with a central extension. We find that the corresponding generating functionals are non-polynomial in the derivatives of the fields with respect to the space-like variable. After constructing models with three- and two-dimensional targets, we study renormalization group flows in this context. In the ultraviolet, in some cases, the target space of the theory reduces to a coset space or there is a fixed point where the theory becomes free

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Canonical equivalence of Liouville and free fields

Abstract: We obtain the parity invariant generating functional for the canonical transformation mapping the Liouville theory into a free scalar field and explain how it is related to the pseudoscalar transformation 1

Cited by 5 publications

References 8 publications

Duality in Quantum Liouville Theory

Duality in Quantum Liouville Theory

Correlation functions and vertex operators of Liouville theory

Duality-invariant class of two-dimensional field theories

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