Liouville theory and logarithmic solutions to knizhnik-zamolodchikov equation

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 ansa...

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Autores principales:	Giribet, G., Simeone, C.
Formato:	JOUR
Materias:	AdS/CFT Conformal field theory String theory
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_0217751X_v20_n20-21_p4821_Giribet
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	todo:paper_0217751X_v20_n20-21_p4821_Giribet
record_format	dspace
spelling	todo:paper_0217751X_v20_n20-21_p4821_Giribet2023-10-03T15:10:33Z Liouville theory and logarithmic solutions to knizhnik-zamolodchikov equation Giribet, G. Simeone, C. AdS/CFT Conformal field theory String theory 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0217751X_v20_n20-21_p4821_Giribet
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	AdS/CFT Conformal field theory String theory
spellingShingle	AdS/CFT Conformal field theory String theory Giribet, G. Simeone, C. Liouville theory and logarithmic solutions to knizhnik-zamolodchikov equation
topic_facet	AdS/CFT Conformal field theory String theory
description	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.
format	JOUR
author	Giribet, G. Simeone, C.
author_facet	Giribet, G. Simeone, C.
author_sort	Giribet, G.
title	Liouville theory and logarithmic solutions to knizhnik-zamolodchikov equation
title_short	Liouville theory and logarithmic solutions to knizhnik-zamolodchikov equation
title_full	Liouville theory and logarithmic solutions to knizhnik-zamolodchikov equation
title_fullStr	Liouville theory and logarithmic solutions to knizhnik-zamolodchikov equation
title_full_unstemmed	Liouville theory and logarithmic solutions to knizhnik-zamolodchikov equation
title_sort	liouville theory and logarithmic solutions to knizhnik-zamolodchikov equation
url	http://hdl.handle.net/20.500.12110/paper_0217751X_v20_n20-21_p4821_Giribet
work_keys_str_mv	AT giribetg liouvilletheoryandlogarithmicsolutionstoknizhnikzamolodchikovequation AT simeonec liouvilletheoryandlogarithmicsolutionstoknizhnikzamolodchikovequation
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Liouville theory and logarithmic solutions to knizhnik-zamolodchikov equation

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