Note on Z{sub 2} symmetries of the KnizhnikZamolodchikov equation
Abstract
We continue the study of hidden Z{sub 2} symmetries of the fourpoint sl(2){sub k} KnizhnikZamolodchikov equation initiated by Giribet [Phys. Lett. B 628, 148 (2005)]. Here, we focus our attention on the fourpoint correlation function in those cases where one spectral flowed state of the sector {omega}=1 is involved. We give a formula that shows how this observable can be expressed in terms of the fourpoint function of non spectral flowed states. This means that the formula holding for the winding violating fourstring scattering processes in AdS{sub 3} has a simple expression in terms of the one for the conservative case, generalizing what is known for the case of threepoint 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 fivepoint function containing a single spectral flow operator to this end. Instead, nondiagonal functional relations between different solutions of the KnizhnikZamolodchikov equation turn out to be the key point for this short path to exist. Considering such functional relation is necessary but it ismore »
 Authors:
 Departamento de Fisica, Universidad de Buenos Aires, FCEN UBA, Ciudad Universitaria, Pabellon I, 1428 Buenos Aires (Argentina)
 Publication Date:
 OSTI Identifier:
 20929615
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Mathematical Physics; Journal Volume: 48; Journal Issue: 1; Other Information: DOI: 10.1063/1.2424789; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ANTI DE SITTER SPACE; CONFORMAL INVARIANCE; CORRELATION FUNCTIONS; EQUATIONS; MATHEMATICAL SOLUTIONS; QUANTUM FIELD THEORY; STRING MODELS; SYMMETRY
Citation Formats
Giribet, Gaston E. Note on Z{sub 2} symmetries of the KnizhnikZamolodchikov equation. United States: N. p., 2007.
Web. doi:10.1063/1.2424789.
Giribet, Gaston E. Note on Z{sub 2} symmetries of the KnizhnikZamolodchikov equation. United States. doi:10.1063/1.2424789.
Giribet, Gaston E. Mon .
"Note on Z{sub 2} symmetries of the KnizhnikZamolodchikov equation". United States.
doi:10.1063/1.2424789.
@article{osti_20929615,
title = {Note on Z{sub 2} symmetries of the KnizhnikZamolodchikov equation},
author = {Giribet, Gaston E.},
abstractNote = {We continue the study of hidden Z{sub 2} symmetries of the fourpoint sl(2){sub k} KnizhnikZamolodchikov equation initiated by Giribet [Phys. Lett. B 628, 148 (2005)]. Here, we focus our attention on the fourpoint correlation function in those cases where one spectral flowed state of the sector {omega}=1 is involved. We give a formula that shows how this observable can be expressed in terms of the fourpoint function of non spectral flowed states. This means that the formula holding for the winding violating fourstring scattering processes in AdS{sub 3} has a simple expression in terms of the one for the conservative case, generalizing what is known for the case of threepoint 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 fivepoint function containing a single spectral flow operator to this end. Instead, nondiagonal functional relations between different solutions of the KnizhnikZamolodchikov 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 WessZuminoNovikovWitten (WZNW) and Liouville conformal theories.},
doi = {10.1063/1.2424789},
journal = {Journal of Mathematical Physics},
number = 1,
volume = 48,
place = {United States},
year = {Mon Jan 15 00:00:00 EST 2007},
month = {Mon Jan 15 00:00:00 EST 2007}
}

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