INVESTIGADORES
SIMEONE Claudio Mauricio
artículos
Título:
Liouville theory and logarithmic solutions to Knizhnik-Zamolodchikov equation.
Autor/es:
GASTON GIRIBET, CLAUDIO SIMEONE
Revista:
INTERNATIONAL JOURNAL OF MODERN PHYSICS A
Editorial:
World Scientific
Referencias:
Año: 2005 vol. 20 p. 4821 - 4862
ISSN:
0217-751X
Resumen:
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
WessZuminoNovikovWitten 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.