Generalized Quantum Current Algebras

Abstract We study the current algebras of the NS5-branes, the Kaluza-Klein (KK) five-branes and the exotic $$ {5}_2^2 $$ 5 2 2 -branes in type IIA/IIB superstring theories. Their worldvolume theories are governed by the six-dimensional $$ \mathcal{N} $$ N = (2, 0) tensor and the $$ \mathcal{N} $$ N = (1, 1) vector multiplets. We show that the current algebras are determined through the S- and T-dualities. The algebras of the $$ \mathcal{N} $$ N = (2, 0) theories are characterized by the Dirac bracket caused by the self-dual gauge field in the five-brane worldvolumes, while those of the $$ \mathcal{N} $$ N = (1, 1) theories are given by the Poisson bracket. By the use of these algebras, we examine extended spaces in terms of tensor coordinates which are the representation of ten-dimensional supersymmetry. We also examine the transition rules of the currents in the type IIA/IIB supersymmetry algebras in ten dimensions. Based on the algebras, we write down the section conditions in the extended spaces and gauge transformations of the supergravity fields.

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Demazure and Weyl Modules for Hyperalgebras of Twisted Current Algebras

Bulletin of the Brazilian Mathematical Society New Series ◽

10.1007/s00574-021-00251-y ◽

2021 ◽

Author(s):

A. Bianchi ◽

T. Macedo

Keyword(s):

Weyl Modules ◽

Current Algebras

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Quantum Conductivity of Spatially Inhomogeneous Systems

MRS Proceedings ◽

10.1557/proc-789-n3.10 ◽

2003 ◽

Vol 789 ◽

Cited By ~ 2

Author(s):

Liudmila A. Pozhar

Keyword(s):

Charge Density ◽

Evolution Equations ◽

Original Method ◽

Theoretical Description ◽

Inhomogeneous System ◽

Inhomogeneous Systems ◽

Spatially Inhomogeneous ◽

Significant Step ◽

Quantum Current ◽

Electro Magnetic

ABSTRACTA fundamental quantum theory of conductivity of spatially inhomogeneous systems in weak electro-magnetic fields has been derived using a two-time Green function (TTGF)-based technique that generalizes the original method due to Zubarev and Tserkovnikov (ZT). Quantum current and charge density evolution equations are derived in a linear approximation with regard to the field potentials. Explicit expressions for the longitudinal and transverse conductivity, and dielectric and magnetic susceptibilities have been derived in terms of charge density - charge density and microcurrent - microcurrent TTGFs. The obtained theoretical description and formulae are applicable to any inhomogeneous system, such as artificial molecules, atomic and molecular clusters, thin films, interfacial systems, etc. In particular, the theory is designed to predict charge transport properties of small semiconductor quantum dots (QDs) and wells (QWs), and is a significant step toward realization of a concept of virtual (i.e., theory-based, computational) synthesis of electronic nanomaterials of prescribed electronic properties.

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INTERACTION OF MESOSCOPIC JOSEPHSON JUNCTION WITH A SUCCESSIVE SQUEEZED COHERENT FIELD

Modern Physics Letters B ◽

10.1142/s021798490000077x ◽

2000 ◽

Vol 14 (16) ◽

pp. 609-618

Author(s):

V. A. POPESCU

Keyword(s):

Coherent State ◽

Josephson Junction ◽

Coherent States ◽

Quantum Noise ◽

Shapiro Steps ◽

Superconducting Ring ◽

Coherent Field ◽

Current Voltage ◽

Quantum Current ◽

The Difference

Signal-to-quantum noise ratio for quantum current in mesoscopic Josephson junction of a circular superconducting ring can be improved if the electromagnetic field is in a successive squeezed coherent state. The mesoscopic Josephson junctions can feel the difference between the successive squeezed coherent states and other types of squeezed coherent states because their current–voltage Shapiro steps are different. We compare our method with another procedure for superposition of two squeezed coherent states (a squeezed even coherent state) and consider the effect of different large inductances on the supercurrent.

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OFF-CRITICAL CURRENT ALGEBRAS

International Journal of Modern Physics A ◽

10.1142/s0217751x95000838 ◽

1995 ◽

Vol 10 (12) ◽

pp. 1717-1736 ◽

Cited By ~ 3

Author(s):

E. ABDALLA ◽

M.C.B. ABDALLA ◽

G. SOTKOV ◽

M. STANISHKOV

Keyword(s):

Abelian Group ◽

Critical Current ◽

General Structure ◽

Dimensional Algebra ◽

Fermionic Model ◽

Infinite Dimensional ◽

Conformally Invariant ◽

Current Algebras

We discuss the infinite-dimensional algebras appearing in integrable perturbations of conformally invariant theories, with special emphasis on the structure of the consequent non-Abelian infinite-dimensional algebra generalizing W∞ to the case of a non-Abelian group. We prove that the pure left sector as well as the pure right sector of the thus-obtained algebra coincides with the conformally invariant case. The mixed sector is more involved, although the general structure seems to be near to being unraveled. We also find some subalgebras that correspond to Kac-Moody algebras. The constraints imposed by the algebras are very strong and, in the case of the massive deformation of a non-Abelian fermionic model, the symmetry alone is enough to fix the two- and three-point functions of the theory.

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W-ALGEBRA REALIZATIONS AND W-GRAVITY ANOMALIES

Modern Physics Letters A ◽

10.1142/s021773239100350x ◽

1991 ◽

Vol 06 (32) ◽

pp. 2995-3003 ◽

Cited By ~ 3

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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