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Title: Free field realization of current superalgebra gl(m vertical bar n){sub k}

Abstract

We construct the free field representation of the affine currents, energy-momentum tensor, and screening currents of the first kind of the current superalgebra gl(m vertical bar n){sub k} uniformly for m=n and m{ne}n. The energy-momentum tensor is given by a linear combination of two Sugawara tensors associated with the two independent quadratic Casimir elements of gl(m vertical bar n)

Authors:
; ;  [1];  [2];  [3]
  1. Institute of Modern Physics, Northwest University, Xian 710069 (China) and Department of Mathematics, University of Queensland, Brisbane, Queensland 4072 (Australia)
  2. (Australia) and Condensed Matter Theory Laboratory, RIKEN, Wako, Saitama 351-0198 (Japan)
  3. (Australia)
Publication Date:
OSTI Identifier:
20929723
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 48; Journal Issue: 5; Other Information: DOI: 10.1063/1.2739306; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; CASIMIR EFFECT; CONFORMAL INVARIANCE; ENERGY-MOMENTUM TENSOR; QUANTUM FIELD THEORY

Citation Formats

Yang Wenli, Zhang Yaozhong, Liu Xin, Department of Mathematics, University of Queensland, Brisbane, Queensland 4072, and Department of Mathematics, University of Queensland, Brisbane, Queensland 4072. Free field realization of current superalgebra gl(m vertical bar n){sub k}. United States: N. p., 2007. Web. doi:10.1063/1.2739306.
Yang Wenli, Zhang Yaozhong, Liu Xin, Department of Mathematics, University of Queensland, Brisbane, Queensland 4072, & Department of Mathematics, University of Queensland, Brisbane, Queensland 4072. Free field realization of current superalgebra gl(m vertical bar n){sub k}. United States. doi:10.1063/1.2739306.
Yang Wenli, Zhang Yaozhong, Liu Xin, Department of Mathematics, University of Queensland, Brisbane, Queensland 4072, and Department of Mathematics, University of Queensland, Brisbane, Queensland 4072. Tue . "Free field realization of current superalgebra gl(m vertical bar n){sub k}". United States. doi:10.1063/1.2739306.
@article{osti_20929723,
title = {Free field realization of current superalgebra gl(m vertical bar n){sub k}},
author = {Yang Wenli and Zhang Yaozhong and Liu Xin and Department of Mathematics, University of Queensland, Brisbane, Queensland 4072 and Department of Mathematics, University of Queensland, Brisbane, Queensland 4072},
abstractNote = {We construct the free field representation of the affine currents, energy-momentum tensor, and screening currents of the first kind of the current superalgebra gl(m vertical bar n){sub k} uniformly for m=n and m{ne}n. The energy-momentum tensor is given by a linear combination of two Sugawara tensors associated with the two independent quadratic Casimir elements of gl(m vertical bar n)},
doi = {10.1063/1.2739306},
journal = {Journal of Mathematical Physics},
number = 5,
volume = 48,
place = {United States},
year = {Tue May 15 00:00:00 EDT 2007},
month = {Tue May 15 00:00:00 EDT 2007}
}
  • We apply the method of the central extensions introduced by Reshetikhin and Semenov{endash}Tian{endash}Shansky to the case of the Perk{endash}Shultz model. By using the method proposed by Frenkel{endash}Ding, we establish the Drinfeld constructions of the quantum affine superalgebra U{sub q}{bold (}gl({cflx m}/n){bold )}. {copyright} {ital 1997 American Institute of Physics.}
  • Using our recent results on eigenvalues of invariants associated to the Lie superalgebra gl(m|n), we use characteristic identities to derive explicit matrix element formulae for all gl(m|n) generators, particularly non-elementary generators, on finite dimensional type 1 unitary irreducible representations. We compare our results with existing works that deal with only subsets of the class of type 1 unitary representations, all of which only present explicit matrix elements for elementary generators. Our work therefore provides an important extension to existing methods, and thus highlights the strength of our techniques which exploit the characteristic identities.
  • Using our recent results on eigenvalues of invariants associated to the Lie superalgebra gl(m|n), we use characteristic identities to derive explicit matrix element formulae for all gl(m|n) generators, particularly non-elementary generators, on finite dimensional type 1 unitary irreducible representations. We compare our results with existing works that deal with only subsets of the class of type 1 unitary representations, all of which only present explicit matrix elements for elementary generators. Our work therefore provides an important extension to existing methods, and thus highlights the strength of our techniques which exploit the characteristic identities.
  • The characteristic identity formalism discussed in our recent articles is further utilized to derive matrix elements of type 2 unitary irreducible gl(m|n) modules. In particular, we give matrix element formulae for all gl(m|n) generators, including the non-elementary generators, together with their phases on finite dimensional type 2 unitary irreducible representations which include the contravariant tensor representations and an additional class of essentially typical representations. Remarkably, we find that the type 2 unitary matrix element equations coincide with the type 1 unitary matrix element equations for non-vanishing matrix elements up to a phase.
  • With the help of the factorizing F-matrix, the scalar products of the U{sub q}(gl(1 vertical bar 1)) free fermion model are represented by determinants. By means of these results, we obtain the determinant representations of correlation functions of the model.