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On the duality of quantum liouville field theory

It has been found empirically that the Virasoro centre and 3-point functions of quantum Liouville field theory with potential e2bΦ(x) and external primary fields exp(αΦ(x)), are invariant with respect to the duality transformations ℏα→q-α where q=b-1+b. The steps leading to this result (via the Vira...

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Main Authors: O'Raifeartaigh, Lochlainn (Author) , Pawlowski, Jan M. (Author) , Sreedhar, Vinnakota (Author)
Format: Article (Journal)
Language:English
Published: 2000
In: International journal of modern physics. A, Particles and fields, gravitation, cosmology
Year: 2000, Volume: 14, Issue: 22n23, Pages: 2401-2409
ISSN:1793-656X
DOI:10.1142/S0217979200001928
Online Access:Verlag, Volltext: http://dx.doi.org/10.1142/S0217979200001928
Verlag, Volltext: http://www.worldscientific.com/doi/abs/10.1142/S0217979200001928
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Author Notes:L. O'raifeartaigh, J.M. Pawlowski, V.V. Sreedhar

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520 |a It has been found empirically that the Virasoro centre and 3-point functions of quantum Liouville field theory with potential e2bΦ(x) and external primary fields exp(αΦ(x)), are invariant with respect to the duality transformations ℏα→q-α where q=b-1+b. The steps leading to this result (via the Virasoro algebra and 3-point functions) are reviewed in the path-integral formalism. The duality stems from the fact that the quantum relationship between the α and the conformal weights Δα is two-to-one. As a result the quantum Liouville potential may actually contain two exponentials (with related parameters). It is shown that in the two-exponential theory the duality appears in a natural way and that an important extrapolation which was previously conjectured can be proved. 
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