scholarly journals Quantum current algebra for the AdS 5 × S 5 superstring

2010 ◽  
Vol 2010 (8) ◽  
Author(s):  
O. A. Bedoya ◽  
D. Z. Marchioro ◽  
D. L. Nedel ◽  
B. Carlini Vallilo
Keyword(s):  
Current Algebra ◽  
Quantum Current

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.

scholarly journals Quantum Current Algebra Symmetries and Integrable Many-Particle Schrödinger Type Quantum Hamiltonian Operators

Symmetry ◽  
2019 ◽  
Vol 11 (8) ◽  
pp. 975
Author(s):  
Dominik Prorok ◽  
Anatolij Prykarpatski
Keyword(s):  
Representation Theory ◽  
Current Algebra ◽  
Fock Space ◽  
Integrable Quantum ◽  
Quantum Hamiltonian ◽  
Quantum Symmetries ◽  
Sutherland Model ◽  
Quantum Current ◽  
Hamiltonian Operators

Based on the G. Goldin’s quantum current algebra symmetry representation theory, have succeeded in explaining a hidden relationship between the quantum many-particle Hamiltonian operators, defined in the Fock space, their factorized structure and integrability. Interesting for applications quantum oscillatory Hamiltonian operators are considered, the quantum symmetries of the integrable quantum Calogero-Sutherland model are analyzed in detail.

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.

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 DEFORMATION OF THE WAKIMOTO CONSTRUCTION

1993 ◽  
Vol 08 (08) ◽  
pp. 715-723 ◽  
Author(s):  
A. ABADA ◽  
A.H. BOUGOURZI ◽  
M.A. EL GRADECHI
Keyword(s):  
Current Algebra ◽  
Quantum Spin ◽  
Vertex Operators ◽  
Free Boson ◽  
Quantum Current ◽  
Boson Fields

We present the extension of the Wakimoto construction to the Uq( su (2)k) quantum current algebra and its associated Zk quantum parafermion algebra. This construction is achieved in terms of various deformations of three classical free boson fields. We also give the vertex operators corresponding to the quantum spin-j representation.

scholarly journals Currents, charges and algebras in exceptional generalised geometry

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
David Osten
Keyword(s):  
Current Algebra ◽  
Hamiltonian Formulation ◽  
Building Blocks ◽  
Lie Derivative ◽  
Consistency Check ◽  
World Volume ◽  
Invariant Currents ◽  
Invariant Current ◽  
M Theory ◽  
A Current

Abstract A classical Ed(d)-invariant Hamiltonian formulation of world-volume theories of half-BPS p-branes in type IIb and eleven-dimensional supergravity is proposed, extending known results to d ≤ 6. It consists of a Hamiltonian, characterised by a generalised metric, and a current algebra constructed s.t. it reproduces the Ed(d) generalised Lie derivative. Ed(d)-covariance necessitates the introduction of so-called charges, specifying the type of p-brane and the choice of section. For p > 2, currents of p-branes are generically non- geometric due to the imposition of U-duality, e.g. the M5-currents contain coordinates associated to the M2-momentum.A derivation of the Ed(d)-invariant current algebra from a canonical Poisson structure is in general not possible. At most, one can derive a current algebra associated to para-Hermitian exceptional geometry.The membrane in the SL(5)-theory is studied in detail. It is shown that in a generalised frame the current algebra is twisted by the generalised fluxes. As a consistency check, the double dimensional reduction from membranes in M-theory to strings in type IIa string theory is performed. Many features generalise to p-branes in SL(p + 3) generalised geometries that form building blocks for the Ed(d)-invariant currents.

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