Abstract:
We study the connection between Zamolodchikov operator-valued relations in Liouville field theory and in the SL(2, ℝ)k WZNW model. In particular, the classical relations in SL(2, ℝ)k can be formulated as a classical Liouville hierarchy in terms of the isotopic coordinates, and their covariance is easily understood in the framework of the AdS3/ CFT2 correspondence. Conversely, we find a closed expression for the classical Liouville decoupling operators in terms of the so-called uniformizing Schwarzian operators and show that the associated uniformizing parameter plays the same role as the isotopic coordinates in SL(2, ℝ)k. The solutions of the jth classical decoupling equation in the WZNW model span a spin j reducible representation of SL(2, ℝ). Likewise, we show that in Liouville theory solutions of the classical decoupling equations span spin j representations of SL(2, ℝ), which is interpreted as the isometry group of the hyperbolic upper half-plane. © 2005 Elsevier B.V. All rights reserved.
Registro:
Documento: |
Artículo
|
Título: | Zamolodchikov relations and Liouville hierarchy in SL(2, R)k WZNW model |
Autor: | Bertoldi, G.; Bolognesi, S.; Giribet, G.; Matone, M.; Nakayama, Y. |
Filiación: | Department of Physics, University of Wales Swansea, Swansea SA2 8PP, United Kingdom Scuola Normale Superiore, Piazza Dei Cavalieri 7, 56126 Pisa, Italy INFN, Sezione di Pisa, Pisa, Italy Universidad de Buenos Aires, Ciudad Universitaria 1428, Pabellon I, Buenos Aires, Argentina Dipartimento di Fisica G. Galilei, Università di Padova, Via Marzolo 8, 35131 Padova, Italy INFN, Sezione di Padova, Padova, Italy Department of Physics, Faculty of Science, University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japan
|
Año: | 2005
|
Volumen: | 709
|
Número: | 3
|
Página de inicio: | 522
|
Página de fin: | 549
|
DOI: |
http://dx.doi.org/10.1016/j.nuclphysb.2005.01.001 |
Título revista: | Nuclear Physics B
|
Título revista abreviado: | Nucl. Phys. B
|
ISSN: | 05503213
|
CODEN: | NUPBB
|
Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_05503213_v709_n3_p522_Bertoldi |
Referencias:
- Zamolodchikov, Al., Higher equations of motion in Liouville field theory hep-th/0312279; Bertoldi, G., Giribet, G., Zamolodchikov operator-valued relations for SL(2,ℝ)k WZNW model (2004) Nucl. Phys. B, 701, p. 481. , hep-th/0405094
- de Boer, J., Ooguri, H., Robins, H., Tannenhauser, J., String theory on AdS3 (1998) JHEP, 9812, p. 026. , hep-th/9812046
- Aharony, O., Gubser, S.S., Maldacena, J., Ooguri, H., Oz, Y., Large N field theories, string theory and gravity (2000) Phys. Rep., 323, pp. 183-386. , hep-th/9905111
- Maldacena, J., Ooguri, H., Strings in AdS3 and the SL(2,ℝ) WZW model. Part 1: The spectrum (2001) J. Math. Phys., 42, pp. 2929-2960. , hep-th/0001053
- Maldacena, J., Ooguri, H., Strings in AdS3 and the SL(2,ℝ) WZW model. Part 3: Correlation functions (2002) Phys. Rev. D, 65, p. 106006. , hep-th/0111180
- Matone, M., Uniformization theory and 2D gravity, 1: Liouville action and intersection numbers (1995) Int. J. Mod. Phys. A, 10, p. 289. , hep-th/9306150
- Bonora, L., Matone, M., KdV equation on Riemann surfaces (1989) Nucl. Phys. B, 327, p. 415
- Benoit, L., Saint-Aubin, Y., Degenerate conformal field theories and explicit expressions for some null vectors (1988) Phys. Lett. B, 215, p. 517
- Bauer, M., Di Francesco, P., Itzykson, C., Zuber, J.-B., Covariant differential equations and singular vectors in Virasoro representations (1991) Nucl. Phys. B, 362, p. 515
- Zograf, P., Takhtajan, L., On uniformization of Riemann surfaces and the Weil-Petersson metric on Teichmüller and Schottky spaces (1988) Math. USSR Sb., 60, pp. 297-313
- Takhtajan, L., Liouville theory: Quantum geometry of Riemann surfaces (1993) Mod. Phys. Lett. A, 8, p. 3529. , hep-th/9308125
- Matone, M., Quantum Riemann surfaces, 2D gravity and the geometrical origin of minimal models (1994) Mod. Phys. Lett. A, 9, p. 2871. , hep-th/9309096
- Matone, M., Nonperturbative model of Liouville gravity (1997) J. Geom. Phys., 21, p. 381. , hep-th/9402081
- Bonelli, G., Marchetti, P.A., Matone, M., Nonperturbative 2D gravity, punctured spheres and theta vacua in string theories (1994) Phys. Lett. B, 339, p. 49. , hep-th/9407091
- Bonelli, G., Marchetti, P.A., Matone, M., Algebraic-geometrical formulation of two-dimensional quantum gravity (1996) Lett. Math. Phys., 36, p. 189. , hep-th/9502089
- Takhtajan, L., Liouville theory: Ward identities for generating functional and modular geometry (1994) Mod. Phys. Lett. A, 9, p. 2293. , hep-th/9403013
- Takhtajan, L., Topics in quantum geometry of Riemann surfaces: Two-dimensional quantum gravity (1994) Como Quantum Groups, pp. 541-580. , hep-th/9409088
- Alvarez-Gaumé, L., Gómez, C., Topics in Liouville theory (1992) Proceedings of the 1991 Trieste Spring School on String Theory and Quantum Gravity, , J. Harvey (Eds.) World Scientific Singapore
- Ginsparg, P., Moore, G., Lectures on 2D Gravity and 2D String Theory, , hep-th/9304011
- Nakayama, Y., Liouville field theory: A decade after the revolution (2004) Int. J. Mod. Phys. A, 19, p. 2771. , hep-th/0402009
- Aganagic, M., Klemm, A., Marino, M., Vafa, C., The topological vertex hep-th/0305132; Aganagic, M., Dijkgraaf, R., Klemm, A., Marino, M., Vafa, C., Topological strings and integrable hierarchies hep-th/0312085; Bonora, L., Lugo, A., Matone, M., Russo, J., A global operator formalism on higher genus Riemann surfaces: B-C systems (1989) Commun. Math. Phys., 123, p. 329
- Gervais, J.-L., Neveu, A., The dual string spectrum in Polyakov's quantization, 1 (1982) Nucl. Phys. B, 199, p. 59
- Gervais, J.-L., Neveu, A., Dual string spectrum in Polyakov's quantization, 2: Mode separation (1982) Nucl. Phys. B, 209, p. 125
- Gervais, J.-L., Neveu, A., New quantum treatment of Liouville field theory (1983) Nucl. Phys. B, 224, p. 329
- Gervais, J.-L., Neveu, A., Novel triangle relation and absence of tachyons in Liouville string field theory (1984) Nucl. Phys. B, 238, p. 125
- Gervais, J.-L., Neveu, A., Green functions and scattering amplitudes in Liouville string field theory, 1 (1984) Nucl. Phys. B, 238, p. 396
- Gervais, J.-L., Neveu, A., Locality in strong coupling Liouville field theory and string models for seven-dimensions, thirteen-dimensions and nineteen-dimensions (1985) Phys. Lett. B, 151, p. 271
- Gervais, J.-L., The quantum group structure of quantum gravity in two-dimensions (1990) Proceedings, Random Surfaces and Quantum Gravity Cargese, pp. 347-361. , see High Energy Physics Index 30 1992 No. 17911
- Teschner, J., Liouville theory revisited (2001) Class. Quantum Grav., 18, pp. R153-R222. , hep-th/0104158
- Teschner, J., Quantum Liouville theory versus quantized Teichmüller spaces (2003) Fortschr. Phys., 51, p. 865. , hep-th/0212243
- Teschner, J., On the relation between quantum Liouville theory and the quantized Teichmüller spaces hep-th/0303149; Teschner, J., A Lecture on the Liouville Vertex Operators, , hep-th/0303150
- Teschner, J., From Liouville theory to the quantum geometry of Riemann surfaces hep-th/0308031; Maldacena, J.M., The large N limit of superconformal field theories and supergravity (1998) Adv. Theor. Math. Phys., 2, pp. 231-252
- Maldacena, J.M., (1999) Int. J. Theor. Phys., 38, pp. 1113-1133. , hep-th/9711200
- Maldacena, J.M., Strominger, A., AdS3 black holes and a stringy exclusion principle (1998) JHEP, 9812, p. 005. , hep-th/9804085
- Giveon, A., Kutasov, D., Seiberg, N., Comments on string theory on AdS3 (1998) Adv. Theor. Math. Phys., 2, p. 733. , hep-th/9806194
- Kutasov, D., Seiberg, N., More comments on string theory on AdS3 (1999) JHEP, 9904, p. 008. , hep-th/9903219
- Ponsot, B., Teschner, J., Liouville bootstrap via harmonic analysis on a non-compact quantum group hep-th/9911110; Ponsot, B., Teschner, J., Clebsch-Gordan and Racah-Wigner coefficients for a continuous series of representations of Uq(sl(2,ℝ)) (2001) Commun. Math. Phys., 224, pp. 613-655. , math.QA/0007097
- Awata, H., Yamada, Y., Fusion rules for the fractional level sl(2) algebra (1992) Mod. Phys. Lett. A, 7, p. 1185
- Di Francesco, P., Itzykson, C., Zuber, J.-B., Classical W-algebras (1991) Commun. Math. Phys., 140, p. 543
Citas:
---------- APA ----------
Bertoldi, G., Bolognesi, S., Giribet, G., Matone, M. & Nakayama, Y.
(2005)
. Zamolodchikov relations and Liouville hierarchy in SL(2, R)k WZNW model. Nuclear Physics B, 709(3), 522-549.
http://dx.doi.org/10.1016/j.nuclphysb.2005.01.001---------- CHICAGO ----------
Bertoldi, G., Bolognesi, S., Giribet, G., Matone, M., Nakayama, Y.
"Zamolodchikov relations and Liouville hierarchy in SL(2, R)k WZNW model"
. Nuclear Physics B 709, no. 3
(2005) : 522-549.
http://dx.doi.org/10.1016/j.nuclphysb.2005.01.001---------- MLA ----------
Bertoldi, G., Bolognesi, S., Giribet, G., Matone, M., Nakayama, Y.
"Zamolodchikov relations and Liouville hierarchy in SL(2, R)k WZNW model"
. Nuclear Physics B, vol. 709, no. 3, 2005, pp. 522-549.
http://dx.doi.org/10.1016/j.nuclphysb.2005.01.001---------- VANCOUVER ----------
Bertoldi, G., Bolognesi, S., Giribet, G., Matone, M., Nakayama, Y. Zamolodchikov relations and Liouville hierarchy in SL(2, R)k WZNW model. Nucl. Phys. B. 2005;709(3):522-549.
http://dx.doi.org/10.1016/j.nuclphysb.2005.01.001