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Abstract:

We study a class of solutions to the SL(2, ℝ)k Knizhnik-Zamolodchikov equation. First, logarithmic solutions which represent four-point correlation functions describing string scattering processes on three-dimensional anti-de Sitter space are discussed. These solutions satisfy the factorization ansatz and include logarithmic dependence on the SL(2, ℝ)-isospin variables. Different types of logarithmic singularities arising are classified and the interpretation of these is discussed. The logarithms found here fit into the usual pattern of the structure of four-point function of other examples of AdS/CFT correspondence. Composite states arising in the intermediate channels can be identified as the phenomena responsible for the appearance of such singularities in the four-point correlation functions. In addition, logarithmic solutions which are related to nonperturbative (finite k) effects are found. By means of the relation existing between four-point functions in Wess-Zumino-Novikov-Witten model formulated on SL(2, ℝ) and certain five-point functions in Liouville quantum conformal field theory, we show how the reflection symmetry of Liouville theory induces particular ℤ2 symmetry transformations on the WZNW correlators. This observation allows to find relations between different logarithmic solutions. This Liouville description also provides a natural explanation for the appearance of the logarithmic singularities in terms of the operator product expansion between degenerate and puncture fields. © World Scientific Publishing Company.

Registro:

Documento: Artículo
Título:Liouville theory and logarithmic solutions to knizhnik-zamolodchikov equation
Autor:Giribet, G.; Simeone, C.
Filiación:Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, United States
Instituto de Astronomía Y Física del Espacio, Departamento de Física, Ciudad Universitaria (1428), Buenos Aires, Argentina
Palabras clave:AdS/CFT; Conformal field theory; String theory
Año:2005
Volumen:20
Número:20-21
Página de inicio:4821
Página de fin:4862
DOI: http://dx.doi.org/10.1142/S0217751X05021270
Título revista:International Journal of Modern Physics A
Título revista abreviado:Int. J. Mod. Phys. A
ISSN:0217751X
CODEN:IMPAE
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0217751X_v20_n20-21_p4821_Giribet

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Citas:

---------- APA ----------
Giribet, G. & Simeone, C. (2005) . Liouville theory and logarithmic solutions to knizhnik-zamolodchikov equation. International Journal of Modern Physics A, 20(20-21), 4821-4862.
http://dx.doi.org/10.1142/S0217751X05021270
---------- CHICAGO ----------
Giribet, G., Simeone, C. "Liouville theory and logarithmic solutions to knizhnik-zamolodchikov equation" . International Journal of Modern Physics A 20, no. 20-21 (2005) : 4821-4862.
http://dx.doi.org/10.1142/S0217751X05021270
---------- MLA ----------
Giribet, G., Simeone, C. "Liouville theory and logarithmic solutions to knizhnik-zamolodchikov equation" . International Journal of Modern Physics A, vol. 20, no. 20-21, 2005, pp. 4821-4862.
http://dx.doi.org/10.1142/S0217751X05021270
---------- VANCOUVER ----------
Giribet, G., Simeone, C. Liouville theory and logarithmic solutions to knizhnik-zamolodchikov equation. Int. J. Mod. Phys. A. 2005;20(20-21):4821-4862.
http://dx.doi.org/10.1142/S0217751X05021270