Note on Z2 symmetries of the Knizhnik-Zamolodchikov equation

Mostrar todas las versiones(3)

We continue the study of hidden Z2 symmetries of the four-point sl (2) k Knizhnik-Zamolodchikov equation initiated by Giribet [Phys. Lett. B 628, 148 (2005)]. Here, we focus our attention on the four-point correlation function in those cases where one spectral flowed state of the sec...

Descripción completa

Guardado en:
Detalles Bibliográficos
Autor principal: Giribet, G.E.
Formato: Artículo publishedVersion
Publicado: 2007
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00222488_v48_n1_p_Giribet
http://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00222488_v48_n1_p_Giribet_oai
Aporte de:
Repositorio Digital de la Universidad de Buenos Aires (UBA) de Universidad de Buenos Aires
id I28-R145-paper_00222488_v48_n1_p_Giribet_oai
record_format dspace
spelling I28-R145-paper_00222488_v48_n1_p_Giribet_oai2020-10-19 Giribet, G.E. 2007 We continue the study of hidden Z2 symmetries of the four-point sl (2) k Knizhnik-Zamolodchikov equation initiated by Giribet [Phys. Lett. B 628, 148 (2005)]. Here, we focus our attention on the four-point correlation function in those cases where one spectral flowed state of the sector ω=1 is involved. We give a formula that shows how this observable can be expressed in terms of the four-point function of non spectral flowed states. This means that the formula holding for the winding violating four-string scattering processes in AdS3 has a simple expression in terms of the one for the conservative case, generalizing what is known for the case of three-point functions, where the violating and the nonviolating structure constants turn out to be connected one to each other in a similar way. What makes this connection particularly simple is the fact that, unlike what one would naively expect, it is not necessary to explicitly solve the five-point function containing a single spectral flow operator to this end. Instead, nondiagonal functional relations between different solutions of the Knizhnik-Zamolodchikov equation turn out to be the key point for this short path to exist. Considering such functional relation is necessary but it is not sufficient; besides, the formula also follows from the relation existing between correlators in both Wess-Zumino-Novikov-Witten (WZNW) and Liouville conformal theories. © 2007 American Institute of Physics. Fil:Giribet, G.E. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. application/pdf http://hdl.handle.net/20.500.12110/paper_00222488_v48_n1_p_Giribet info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar J. Math. Phys. 2007;48(1) Note on Z2 symmetries of the Knizhnik-Zamolodchikov equation info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion http://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00222488_v48_n1_p_Giribet_oai
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-145
collection Repositorio Digital de la Universidad de Buenos Aires (UBA)
description We continue the study of hidden Z2 symmetries of the four-point sl (2) k Knizhnik-Zamolodchikov equation initiated by Giribet [Phys. Lett. B 628, 148 (2005)]. Here, we focus our attention on the four-point correlation function in those cases where one spectral flowed state of the sector ω=1 is involved. We give a formula that shows how this observable can be expressed in terms of the four-point function of non spectral flowed states. This means that the formula holding for the winding violating four-string scattering processes in AdS3 has a simple expression in terms of the one for the conservative case, generalizing what is known for the case of three-point functions, where the violating and the nonviolating structure constants turn out to be connected one to each other in a similar way. What makes this connection particularly simple is the fact that, unlike what one would naively expect, it is not necessary to explicitly solve the five-point function containing a single spectral flow operator to this end. Instead, nondiagonal functional relations between different solutions of the Knizhnik-Zamolodchikov equation turn out to be the key point for this short path to exist. Considering such functional relation is necessary but it is not sufficient; besides, the formula also follows from the relation existing between correlators in both Wess-Zumino-Novikov-Witten (WZNW) and Liouville conformal theories. © 2007 American Institute of Physics.
format Artículo
Artículo
publishedVersion
author Giribet, G.E.
spellingShingle Giribet, G.E.
Note on Z2 symmetries of the Knizhnik-Zamolodchikov equation
author_facet Giribet, G.E.
author_sort Giribet, G.E.
title Note on Z2 symmetries of the Knizhnik-Zamolodchikov equation
title_short Note on Z2 symmetries of the Knizhnik-Zamolodchikov equation
title_full Note on Z2 symmetries of the Knizhnik-Zamolodchikov equation
title_fullStr Note on Z2 symmetries of the Knizhnik-Zamolodchikov equation
title_full_unstemmed Note on Z2 symmetries of the Knizhnik-Zamolodchikov equation
title_sort note on z2 symmetries of the knizhnik-zamolodchikov equation
publishDate 2007
url http://hdl.handle.net/20.500.12110/paper_00222488_v48_n1_p_Giribet
http://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00222488_v48_n1_p_Giribet_oai
work_keys_str_mv AT giribetge noteonz2symmetriesoftheknizhnikzamolodchikovequation
_version_ 1766026599698792448

Ejemplares similares