On the “Drinfeld-Sokolov” Reduction of the Knizhnik-Zamolodchikov Equation

1993 ◽  
pp. 131-141 ◽  
Author(s):  
P. Furlan ◽  
A. Ch. Ganchev ◽  
R. Paunov ◽  
V. B. Petkova
Keyword(s):  
Zamolodchikov Equation

scholarly journals Kontsevich’s integral for the Kauffman polynomial

1996 ◽  
Vol 142 ◽  
pp. 39-65 ◽  
Author(s):  
Thang Tu Quoc Le ◽  
Jun Murakami
Keyword(s):  
Finite Type ◽  
Knot Invariants ◽  
Chord Diagrams ◽  
Knot Invariant ◽  
Kauffman Polynomial ◽  
Zamolodchikov Equation

Kontsevich’s integral is a knot invariant which contains in itself all knot invariants of finite type, or Vassiliev’s invariants. The value of this integral lies in an algebra A0, spanned by chord diagrams, subject to relations corresponding to the flatness of the Knizhnik-Zamolodchikov equation, or the so called infinitesimal pure braid relations [11].

scholarly journals EMPTINESS FORMATION PROBABILITY AND QUANTUM KNIZHNIK-ZAMOLODCHIKOV EQUATION

2004 ◽  
Vol 19 (supp02) ◽  
pp. 57-81
Author(s):  
H. E. BOOS ◽  
V. E. KOREPIN ◽  
F. A. SMIRNOV
Keyword(s):  
Quantum Correlations ◽  
Zero Magnetic Field ◽  
Heisenberg Antiferromagnet ◽  
Zero Temperature ◽  
One Dimensional ◽  
Formation Probability ◽  
Antiferromagnetic Ground State ◽  
A New Technique ◽  
The One ◽  
Zamolodchikov Equation

We consider the one-dimensional XXX spin 1/2 Heisenberg antiferromagnet at zero temperature and zero magnetic field. We are interested in a probability of a formation of a ferromagnetic string P(n) in the antiferromagnetic ground-state. We call it emptiness formation probability [EFP]. We suggest a new technique for computation of the EFP in the inhomogeneous case. It is based on the quantum Knizhnik-Zamolodchikov equation [qKZ]. We calculate EFP for n≤6 for the inhomogeneous case. The homogeneous limit confirms our hypothesis about the relation of quantum correlations and number theory. We also make a conjecture about a structure of EFP for arbrary n.

scholarly journals Gauge Dressing of 2D Field Theories

1997 ◽  
Vol 12 (13) ◽  
pp. 2425-2436 ◽  
Author(s):  
Ian I. Kogan ◽  
Alex Lewis ◽  
Oleg A. Soloviev
Keyword(s):  
Correlation Functions ◽  
Field Theories ◽  
Ward Identities ◽  
Zamolodchikov Equation

By using the gauge Ward identities, we study correlation functions of gauged WZNW models. We show that the gauge dressing of the correlation functions can be taken into account as a solution of the Knizhnik–Zamolodchikov equation. Our method is analogous to the analysis of the gravitational dressing of 2D field theories.

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