Free field realization of the level-2 elliptic algebra $$U_{x,p} (\widehat{\mathfrak{s}\mathfrak{l}}_2 )*)$$

2005 ◽  
Vol 55 (11) ◽  
pp. 1455-1460 ◽  
Author(s):  
Hitoshi Konno
Keyword(s):  
Free Field ◽  
Free Field Realization ◽  
Elliptic Algebra ◽  
Level 2

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.

SPECTRAL FLOW AND FREE FIELD REALIZATIONS OF BOSONIC STRINGS ON NAPPI–WITTEN GROUP MANIFOLD

2011 ◽  
Vol 26 (01) ◽  
pp. 149-160
Author(s):  
GANG CHEN
Keyword(s):  
Lie Algebra ◽  
Bosonic Strings ◽  
Free Field ◽  
Geometric Interpretation ◽  
Closed String ◽  
Space Time ◽  
Spectral Flow ◽  
Affine Lie Algebra ◽  
Group Manifold ◽  
Free Field Realization

In this paper we study some aspects of closed string theories in the Nappi–Witten space–time. The effects of spectral flow on the geodesics are studied in terms of an explicit parametrization of the group manifold. The worldsheets of the closed strings under the spectral flow of the geodesics can be classified into four classes, each with a geometric interpretation. We also obtain a free field realization of the Nappi–Witten affine Lie algebra in the most general conditions using a different but equivalent parametrization of the group manifold.

QUANTUM HAMILTONIAN REDUCTION AND WB ALGEBRA

1992 ◽  
Vol 07 (20) ◽  
pp. 4885-4898 ◽  
Author(s):  
KATSUSHI ITO
Keyword(s):  
Lie Algebras ◽  
Free Field ◽  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Hamiltonian Reduction ◽  
Affine Lie Algebras ◽  
Quantum Hamiltonian Reduction ◽  
Free Field Realization ◽  
Coset Construction ◽  
Quantum Hamiltonian

We study the quantum Hamiltonian reduction of affine Lie algebras and the free field realization of the associated W algebra. For the nonsimply laced case this reduction does not agree with the usual coset construction of the W minimal model. In particular, we find that the coset model [Formula: see text] can be obtained through the quantum Hamiltonian reduction of the affine Lie superalgebra B(0, n)(1). To show this we also construct the Feigin-Fuchs representation of affine Lie superalgebras.

scholarly journals Free field realization of N = 2 super-W3 algebra

1993 ◽  
Vol 304 (3-4) ◽  
pp. 271-277 ◽  
Author(s):  
Katsushi Ito
Keyword(s):  
Free Field ◽  
Free Field Realization

scholarly journals WAKIMOTO REALIZATION OF THE ELLIPTIC QUANTUM GROUP $U_{q,p}(\widehat{{\rm sl}_N})$

2009 ◽  
Vol 24 (30) ◽  
pp. 5561-5578
Author(s):  
TAKEO KOJIMA
Keyword(s):  
Quantum Group ◽  
Free Field ◽  
Quantum Algebra ◽  
Free Field Realization ◽  
Wakimoto Realization ◽  
Arbitrary Level ◽  
Elliptic Quantum

We construct a free field realization of the elliptic quantum algebra [Formula: see text] for arbitrary level k ≠ 0, -N. We study Drinfeld current and the screening current associated with [Formula: see text] for arbitrary level k. In the limit p → 0 this realization becomes q-Wakimoto realization for [Formula: see text].

scholarly journals Free field realization of D-brane in group manifold

2000 ◽  
Vol 2000 (08) ◽  
pp. 044-044 ◽  
Author(s):  
Hiroshi Ishikawa ◽  
Satoshi Watamura
Keyword(s):  
Free Field ◽  
Group Manifold ◽  
Free Field Realization

scholarly journals A REMARK ON GROUND STATE OF BOUNDARY IZERGIN–KOREPIN MODEL

2011 ◽  
Vol 26 (12) ◽  
pp. 1973-1989 ◽  
Author(s):  
TAKEO KOJIMA
Keyword(s):  
Ground State ◽  
Free Field ◽  
Baxter Equation ◽  
R Matrix ◽  
Free Field Realization ◽  
Matrix Formula ◽  
K Matrix

We study the ground state of the boundary Izergin–Korepin model. The boundary Izergin–Korepin model is defined by the so-called R-matrix and K-matrix for [Formula: see text] which satisfy Yang–Baxter equation and boundary Yang–Baxter equation. The ground state associated with identity K-matrix [Formula: see text] was constructed by W.-L. Yang and Y.-Z. Zhang in earlier study. We construct the free field realization of the ground state associated with nontrivial diagonal K-matrix.

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