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 TMF, 2000, Volume 123, Number 2, Pages 299–307 (Mi tmf604)

The duality of quantum Liouville field theory

L. O'Raifeartaigh, J. M. Pawlowski, V. V. Sreedhar

Abstract: It has been found empirically that the Virasoro center and three-point functions of quantum Liouville field theory with the potential $\exp(2b\phi(x))$ and the external primary fields $\exp(\alpha\phi(x))$ are invariant with respect to the duality transformations $\hbar\alpha\rightarrow q-\alpha$, where $q=b^{-1}+b$. The steps leading to this result (via the Virasoro algebra and three-point functions) are reviewed in the path-integral formalism. The duality occurs because the quantum relationship between the $\alpha$ and the conformal weights $\Delta_\alpha$ is two-to-one. As a result, the quantum Liouville potential can actually contain two exponentials (with related parameters). In the two-exponential theory, the duality appears naturally, and an important previously conjectured extrapolation can be proved.

DOI: https://doi.org/10.4213/tmf604

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English version:
Theoretical and Mathematical Physics, 2000, 123:2, 663–670

Bibliographic databases:

Citation: L. O'Raifeartaigh, J. M. Pawlowski, V. V. Sreedhar, “The duality of quantum Liouville field theory”, TMF, 123:2 (2000), 299–307; Theoret. and Math. Phys., 123:2 (2000), 663–670

Citation in format AMSBIB
\Bibitem{OraPawSre00} \by L.~O'Raifeartaigh, J.~M.~Pawlowski, V.~V.~Sreedhar \paper The duality of quantum Liouville field theory \jour TMF \yr 2000 \vol 123 \issue 2 \pages 299--307 \mathnet{http://mi.mathnet.ru/tmf604} \crossref{https://doi.org/10.4213/tmf604} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1794162} \zmath{https://zbmath.org/?q=an:1031.81632} \transl \jour Theoret. and Math. Phys. \yr 2000 \vol 123 \issue 2 \pages 663--670 \crossref{https://doi.org/10.1007/BF02551399} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000165897000010} 

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1. Blaszak M., “From bi-Hamiltonian geometry to separation of variables: Stationary Harry-Dym and the KdV dressing chain”, Journal of Nonlinear Mathematical Physics, 9 (2002), 1–13, Suppl. 1
2. Blaszak, M, “Separability preserving Dirac reductions of Poisson pencils on Riemannian manifolds”, Journal of Physics A-Mathematical and General, 36:5 (2003), 1337
3. Giribet G.E., Lopez-Fogliani D.E., “Remarks on free field realization of SL(2, R)(k)/U(1) x U(1) WZNW model”, Journal of High Energy Physics, 2004, no. 6, 026
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