scholarly journals A FREE FIELD REPRESENTATION OF THE SCREENING CURRENTS OF $U_q (\widehat{{\rm sl}(3)})$

1995 ◽  
Vol 10 (04) ◽  
pp. 561-578 ◽  
Author(s):  
A. H. BOUGOURZI ◽  
ROBERT A. WESTON
Keyword(s):  
Current Algebra ◽  
Free Field ◽  
Quantum Affine Algebra ◽  
Affine Algebra ◽  
Field Representation ◽  
Independent Screening ◽  
Quantum Current ◽  
Quantum Analog ◽  
Wakimoto Realization ◽  
Infinite Sum

We construct five independent screening currents associated with the [Formula: see text] quantum current algebra. The screening currents are expressed as exponentials of the eight basic deformed bosonic fields that are required in the quantum analog of the Wakimoto realization of the current algebra. Four of the screening currents are "simple," in that each one is given as a single exponential field. The fifth is expressed as an infinite sum of exponential fields. For reasons which we will discuss, we expect that the structure of the screening currents for a general quantum affine algebra will be similar to the [Formula: see text] case.

BRST COHOMOLOGY IN QUANTUM AFFINE ALGEBRA $U_q \left( {\widehat{sl_2 }} \right)$

1994 ◽  
Vol 09 (14) ◽  
pp. 1253-1265 ◽  
Author(s):  
HITOSHI KONNO
Keyword(s):  
Free Field ◽  
Classical Case ◽  
Explicit Construction ◽  
Quantum Affine Algebra ◽  
Affine Algebra ◽  
Field Representation ◽  
Highest Weight ◽  
Brst Charge ◽  
Brst Cohomology ◽  
Highest Weight Representation

Using free field representation of quantum affine algebra [Formula: see text], we investigate the structure of the Fock modules over [Formula: see text]. The analysis is based on a q-analog of the BRST formalism given by Bernard and Felder in the affine Kac-Moody algebra [Formula: see text]. We give an explicit construction of the singular vectors using the BRST charge. By the same cohomology analysis as the classical case (q=1), we obtain the irreducible highest weight representation space as a non-trivial cohomology group. This enables us to calculate a trace of the q-vertex operators over this space.

scholarly journals Twisted sl(3,C)(2)k current algebra: free field representation and screening currents

2001 ◽  
Vol 523 (3-4) ◽  
pp. 367-376 ◽  
Author(s):  
Xiang-Mao Ding ◽  
Mark D. Gould ◽  
Yao-Zhong Zhang
Keyword(s):  
Current Algebra ◽  
Free Field ◽  
Field Representation ◽  
K Current

scholarly journals A QUANTUM ANALOG OF THE BOSON–FERMION CORRESPONDENCE

1995 ◽  
Vol 10 (07) ◽  
pp. 923-942 ◽  
Author(s):  
A. HAMID BOUGOURZI ◽  
LUC VINET
Keyword(s):  
Current Algebra ◽  
Quantum Case ◽  
Fermionic Field ◽  
Classical Correspondence ◽  
Quantum Current ◽  
Quantum Analog ◽  
Level 2

We review the classical boson-fermion correspondence in the context of the [Formula: see text] current algebra at level 2. This particular algebra is ideal for exhibiting this correspondence because it can be realized either in terms of three real bosonic fields or in terms of one real and one complex fermionic field. We also derive a fermionic realization of the quantum current algebra [Formula: see text] at level 2 and by comparing this realization with the existing bosonic one we extend the classical correspondence to the quantum case.

scholarly journals THE FREE FIELD REPRESENTATION OF SU(3) CONFORMAL FIELD THEORY

1993 ◽  
Vol 08 (23) ◽  
pp. 4031-4053
Author(s):  
HOVIK D. TOOMASSIAN
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Correlation Functions ◽  
Free Field ◽  
Field Representation ◽  
Conformal Field ◽  
Point Correlation

The structure of the free field representation and some four-point correlation functions of the SU(3) conformal field theory are considered.

W-ALGEBRA REALIZATIONS AND W-GRAVITY ANOMALIES

1991 ◽  
Vol 06 (32) ◽  
pp. 2995-3003 ◽  
Author(s):  
C. M. HULL ◽  
L. PALACIOS
Keyword(s):  
Path Integral ◽  
Current Algebra ◽  
Gravity Anomalies ◽  
Normal Ordering ◽  
Path Integral Quantization ◽  
Transformation Rules ◽  
Higher Derivative ◽  
Quantum Current ◽  
Boson Model ◽  
Background Charge

The coupling of scalars fields to chiral W3 gravity is reviewed. In general the quantum current algebra generated by the spin-two and three currents does not close when the "natural" regularization (corresponding to the normal ordering with respect to the modes of ∂ϕi) is used, and the non-closure reflects matter-dependent anomalies in the path integral quantization. We consider the most general modification of the current, involving higher derivative "background charge" terms, and find the conditions for them to form a closed algebra in the "natural" regularization. These conditions can be satisfied only for the two-boson model. In that case, it is possible to cancel all the matter-dependent anomalies by adding finite local counter terms to the action and modifying the transformation rules of the fields.

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