SOME INTEGRAL FORMULAS FOR THE SOLUTIONS OF THE sl2 dKZ EQUATION WITH LEVEL −4

1994 ◽  
Vol 09 (32) ◽  
pp. 5673-5687 ◽  
Author(s):  
ATSUSHI NAKAYASHIKI
Keyword(s):  
Correlation Function ◽  
Integral Formula ◽  
Time Integration ◽  
Direct Proof ◽  
Vertex Operators ◽  
Type I ◽  
Xxz Model ◽  
Integral Formulas ◽  
Xxx Model

A direct proof is given for the fact that the integral formula for the XXX limit of the trace of the type I q-vertex operators satisfies the deformed Knizhnik-Zamolodchikov (dKZ) equation with level −4. We have also carried out one-time integration by taking the residue at infinity. As a corollary of these we can construct a family of the integral formulas for solutions to the dKZ equation. Another corollary is the integral formula for the correlation function of the inhomogeneous XXX model, whose number of integrals is less than that of the previously obtained correlator for the XXZ model.

scholarly journals From Quantum Affine Groups to the Exact Dynamical Correlation Function of the Heisenberg Model

1997 ◽  
Vol 11 (01n02) ◽  
pp. 103-107
Author(s):  
A. H. Bougourzi ◽  
M. Couture ◽  
M. Kacir
Keyword(s):  
Correlation Function ◽  
Form Factors ◽  
Exact Formula ◽  
Exact Form ◽  
Zero Temperature ◽  
Dynamical Correlation ◽  
Xxz Model ◽  
Affine Groups ◽  
Affine Symmetry ◽  
Xxx Model

The exact form factors of the Heisenberg models XXX and XXZ have been recently computed through the quantum affine symmetry of XXZ model in the thermodynamic limit. We use them to derive an exact formula for the contribution of two spinons to the dynamical correlation function of XXX model at zero temperature.

scholarly journals Correlation function diagnostics for type-I fracton phases

2018 ◽  
Vol 97 (4) ◽  
Author(s):  
Trithep Devakul ◽  
S. A. Parameswaran ◽  
S. L. Sondhi
Keyword(s):  
Correlation Function ◽  
Type I

ON THE TWO-POINT CORRELATION FUNCTION FOR DISPERSIONS OF NONOVERLAPPING SPHERES

1998 ◽  
Vol 08 (02) ◽  
pp. 359-377 ◽  
Author(s):  
KONSTANTIN Z. MARKOV ◽  
JOHN R. WILLIS
Keyword(s):  
Distribution Function ◽  
Correlation Function ◽  
Characteristic Function ◽  
Radial Distribution Function ◽  
Radial Distribution ◽  
Integral Formula ◽  
Probability Densities ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Point Level

Random dispersions of spheres are useful and appropriate models for a wide class of particulate random materials. They can be described in two equivalent and alternative ways — either by the multipoint moments of the characteristic function of the region, occupied by the spheres, or by the probability densities of the spheres' centers. On the "two-point" level, a simple and convenient integral formula is derived which interconnects the radial distribution function of the spheres with the two-point correlation of the said characteristic function. As one of the possible applications of the formula, the behavior of the correlation function near the origin is studied in more detail and related to the behavior of the radial distribution function at the "touching" separation of the spheres.

FUSION CONSTRUCTION OF THE VERTEX OPERATORS IN HIGHER LEVEL REPRESENTATION OF THE ELLIPTIC QUANTUM GROUP

2002 ◽  
Vol 16 (14n15) ◽  
pp. 1995-2001
Author(s):  
HITOSHI KONNO
Keyword(s):  
Quantum Group ◽  
Free Field ◽  
Vertex Operators ◽  
Type I ◽  
Field Representation ◽  
Short Summary ◽  
Higher Spin ◽  
Elliptic Algebra ◽  
Elliptic Quantum ◽  
Weight Coefficients

After a short summary on the elliptic quantum group [Formula: see text] and the elliptic algebra [Formula: see text], we present a free field representation of the Drinfeld currents and the vertex operators (VO's) in the level k. We especially demonstrate a construction of the higher spin type I VO's by fusing the spin 1/2 type I VO's and fix a rule of attaching the screening current S(z) associated with the q-deformed ℤk-parafermion theory. As a result we get a free field representation of the higher spin type I VO's which commutation relation by the fused Boltzmann weight coefficients is manifest.

scholarly journals The large-c Virasoro identity block is a semi-classical Liouville correlator

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Gideon Vos
Keyword(s):  
Correlation Function ◽  
Liouville Equation ◽  
Classical Limit ◽  
Central Charge ◽  
Equation Of Motion ◽  
Einstein Gravity ◽  
Liouville Theory ◽  
Vertex Operators

Abstract It will be shown analytically that the light sector of the identity block of a mixed heavy-light correlator in the large central charge limit is given by a correlation function of light operators on an effective background geometry. This geometry is generated by the presence of the heavy operators. It is shown that this background geometry is a solution to the Liouville equation of motion sourced by corresponding heavy vertex operators and subsequently that the light sector of the identity block matches the Liouville correlation function in the semi-classical limit. This method effectively captures the spirit of Einstein gravity as a theory of dynamical geometry in AdS/CFT. The reason being that Liouville theory is closely related to semi-classical asymptotically AdS3 gravity.

scholarly journals Integral formulas with weight factors

1992 ◽  
Vol 52 (1) ◽  
pp. 26-39
Author(s):  
Telemachos Hatziafratis
Keyword(s):  
Complete Intersection ◽  
Integral Formula ◽  
Integral Formulas ◽  
Weight Factors ◽  
Type Integral

AbstractA Bochner-Martinelli-Koppelman type integral formula with weight factors is derived on complete intersection submanifolds of domains of Cn.

EXCHANGE RELATIONS OF LEVEL-TWO VERTEX OPERATORS OF $U_q (\widehat{{\rm sl}_2})$

2003 ◽  
Vol 18 (06) ◽  
pp. 901-916
Author(s):  
WEN-LI YANG
Keyword(s):  
Vertex Operators ◽  
Type I ◽  
Exchange Relations

We calculate the exchange relations of vertex operators of [Formula: see text] at level-two from their bosonic realization. We also study the corresponding invertibility relation of type I vertex operators.

scholarly journals FREE FIELD CONSTRUCTIONS FOR THE ELLIPTIC ALGEBRA $\rscr{A}_{q,p}(\widehat{sl}_2)$ AND BAXTER'S EIGHT-VERTEX MODEL

2004 ◽  
Vol 19 (supp02) ◽  
pp. 363-380 ◽  
Author(s):  
J. SHIRAISHI
Keyword(s):  
Integral Formula ◽  
Free Field ◽  
Virasoro Algebra ◽  
Vertex Operators ◽  
Vertex Model ◽  
Elliptic Algebra ◽  
Deformed Virasoro Algebra ◽  
The One ◽  
Level 2 ◽  
Elliptic Quantum

Three examples of free field constructions for the vertex operators of the elliptic quantum group [Formula: see text] are obtained. Two of these ( for p1/2=±q3/2, p1/2=-q2) are based on representation theories of the deformed Virasoro algebra, which correspond to the level 4 and level 2 Z-algebra of Lepowsky and Wilson. The third one (p1/2=q3) is constructed over a tensor product of a bosonic and a fermionic Fock spaces. The algebraic structure at (p1/2=q3), however, is not related to the deformed Virasoro algebra. Using these free field constructions, an integral formula for the correlation functions of Baxter's eight-vertex model is obtained. This formula shows different structure compared with the one obtained by Lashkevich and Pugai.

Sign in / Sign up

Export Citation Format

Share Document