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The duality of quantum Liouville field theory

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Abstract

It has been found empirically that the Virasoro center and three-point functions of quantum Liouville field theory with the potential exp(2bϕ(x)) and the 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 three-point functions) are reviewed in the path-integral formalism. The duality occurs because the quantum relationship between the α and the conformal weights Δα 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.

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References

  1. H. Poincaré,J. Math. Pure Appl.,5, No. 4, 157 (1898).

    Google Scholar 

  2. A. Polyakov,Phys. Lett. B,103, 207 (1981).

    Article  ADS  MathSciNet  Google Scholar 

  3. J.-L. Gervais and A. Neveu,Nucl. Phys. B,238, 125 (1984).

    Article  ADS  MathSciNet  Google Scholar 

  4. H. Dorn and H.-J. Otto,Phys. Lett. B,291, 39 (1992);Nucl. Phys. B,429, 375 (1994).

    Article  ADS  MathSciNet  Google Scholar 

  5. A. Zamolodchikov and Al. Zamolodchikov,Nucl. Phys. B,477, 577 (1996); L. Baulieu, V. Kazakov, M. Picco, and P. Windey, eds.,Low Dimensional Applications of Quantum Field Theory (NATO ASI series B, Physics Vol. 362), Plenum (1997); J.-L. Gervais and A. Neveu,Nucl. Phys. B,238, 396 (1984);257 [FS14], 59 (1985).

    Article  ADS  MathSciNet  Google Scholar 

  6. T. Curtright and C. Thorn,Phys. Rev. Lett.,48, 1309 (1982).

    Article  ADS  MathSciNet  Google Scholar 

  7. E. Braaten, T. Curtright, and C. Thorn,Phys. Lett.,118, 115 (1982);Ann. Phys.,147, 365 (1983).

    Article  MathSciNet  Google Scholar 

  8. E. D’Hoker and R. Jackiw,Phys. Rev. D,26, 3517 (1982).

    Article  ADS  MathSciNet  Google Scholar 

  9. M. Goulian and M. Li,Phys. Rev. Lett.,66, 2051 (1991).

    Article  ADS  Google Scholar 

  10. Vl. Dotsenko and V. Fateev,Nucl. Phys. B,251, 691 (1985).

    ADS  MathSciNet  Google Scholar 

  11. J. Teschner,Phys. Lett. B,363, 65 (1995).

    Article  ADS  Google Scholar 

  12. L. O’Raifeartaigh, J. M. Pawlowski, and V. V. Sreedhar, “Duality in quantum Liouville theory,” Preprint hep-th/9811090 (1998).

  13. S. Dotsenko,Mod. Phys. Lett. A,6, 3601 (1991).

    Article  ADS  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Dublin Institute for Advanced Studies, Dublin, Ireland

    L. O’Raifeartaigh, J. M. Pawlowski & V. V. Sreedhar

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  1. L. O’Raifeartaigh
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  2. J. M. Pawlowski
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  3. V. V. Sreedhar
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 123, No. 2, pp. 299–307, May, 2000.

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O’Raifeartaigh, L., Pawlowski, J.M. & Sreedhar, V.V. The duality of quantum Liouville field theory. Theor Math Phys 123, 663–670 (2000). https://doi.org/10.1007/BF02551399

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