Remark on the reflection coefficient in the Liouville model

Abstract

We show that the reflection coefficients in the quantum theory of the Liouville model calculated in the bootstrap and Hamiltonian approaches differ from each other by a phase factor and simply yield different normalizations of vertex operators.

This is a preview of subscription content, log in to check access.

References

  1. 1.

    A. B. Zamolodchikov and Al. B. Zamolodchikov, “Conformal bootstrap in Liouville field theory,” Nucl. Phys. B, 477, 577–605 (1996); “Structure constants and conformal bootstrap in Liouville field theory,” arXiv:hep-th/9506136v2 (1995).

    ADS  MathSciNet  Article  MATH  Google Scholar 

  2. 2.

    L. D. Faddeev and L. A. Takhtajan, “Liouville model on the lattice,” in: Field Theory, Quantum Gravity, and Strings (Lect. Notes Phys., Vol. 246, H. J. de Vega and N. Sanchez, eds.), Springer, Berlin (1986), pp. 166–179.

    Google Scholar 

  3. 3.

    J. Teschner, “Liouville theory revisited,” Class. Q. Grav., 18, R153–R222 (2001); arXiv:hep-th/0104158v3 (2001).

    ADS  MathSciNet  Article  MATH  Google Scholar 

  4. 4.

    L. D. Faddeev and A. Yu. Volkov, “Discrete evolution for the zero-modes of the quantum Liouville model,” J. Phys. A, 41, 194008 (2008); arXiv:0803.0230v1 [hep-th] (2008).

    ADS  MathSciNet  Article  MATH  Google Scholar 

  5. 5.

    L. D. Faddeev, “Zero modes for the quantum Liouville model,” Funct. Anal. Appl., 48, 166–174 (2014); arXiv:1404.1713v1 [hep-th] (2014).

    MathSciNet  Article  MATH  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to S. E. Derkachev.

Additional information

This research is supported by a grant from the Russian Science Foundation (Project No. 14-11-00598).

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 192, No. 2, pp. 221–226, August, 2017.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Derkachev, S.E., Faddeev, L.D. Remark on the reflection coefficient in the Liouville model. Theor Math Phys 192, 1129–1133 (2017). https://doi.org/10.1134/S0040577917080037

Download citation

Keywords

  • Liouville quantum model
  • conformal bootstrap
  • conformal field theory