Classical affine algebras

Feingold, Alex J.; Frenkel, Igor

doi:10.1016/0001-8708(85)90027-1

Cited by 107 publications

(85 citation statements)

References 6 publications

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“…(For a review see ref. [21].) From now on, we shall specialize to the case of simply laced G. (The more complicated case of non-simply laced algebras has been treated in ref.…”

Section: Mass Spectrummentioning

confidence: 99%

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Locally supersymmetric σ-model with Wess-Zumino term in two dimensions and critical dimensions for strings

et al. 1986

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Locally supersymmetric σ-model with Wess-Zumino term in two dimensions and critical dimensions for strings Bergshoeff, Eric; Randjbar-Daemi, S.; Salam, A.; Sarmadi, H.; Sezgin, E. Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the number of authors shown on this cover page is limited to 10 maximum. We construct an N = 1 locally supersymmetnc o-model with a Wess-Zummo term coupled to supergravity m two dimensions. If one takes the o-model mamfold to be the product of d-d~mensmnal Minkowski space M a and a group mamfold G, and if the radms of G is quantized m appropriate umts of the stnng tensmn, then the model descnbes a Neveu-Schwarz-Ramond (NSR)-type string mowng on M d × G (Our model generahzes earlier work of refs. [1,2] which do not contain a Wess-Zumino term and that of refs [5,6] which is not locally supersymmetnc ) The zwetbein and the gravitmo field equations yteld constraints which generahze those of the NSR model to the case of a non-abelian group mamfold In particular, the fenmomc constraint contains a new term tnlinear m the fermiomc fields We quantize the theory in the light-cone gauge and derive the critical dimensions. We compute the mass spectrum of a closed stnng moving on M a × G and show that massless fermmns do not arise for non-abdian G for the spmmng stnng, in agreement with the result of Friedan and Shenker [22] * Supported by Swiss National Funds.

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“…(For a review see ref. [21].) From now on, we shall specialize to the case of simply laced G. (The more complicated case of non-simply laced algebras has been treated in ref.…”

Section: Mass Spectrummentioning

confidence: 99%

“…From now on, we shall specialize to the case of simply laced G. (The more complicated case of non-simply laced algebras has been treated in ref. [21].) Furthermore we restrict ourselves to k = 1.…”

Section: Mass Spectrummentioning

confidence: 99%

Locally supersymmetric σ-model with Wess-Zumino term in two dimensions and critical dimensions for strings

et al. 1986

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“…Since we are dealing here with a supersymmetric system, it will be useful to review the basics of Lie superalgebras [54][55][56][57][58][59][60][61][62][63][64][65]. In terms of the Weyl matrices e ij ∈ End (V ) − matrices whose elements are all zero, except that one on the ith line and jth column, which equals 1 − and always considering a sum on the repeated indices, we can define, in a Z 2 -graded Lie algebra, the graded tensor product of two homogeneous even elements A ∈ End (V ) and B ∈ End (V )…”

Section: (Although Its Hamiltonianmentioning

confidence: 99%

“…We highlight that vertex-models associated with Lie superalgebras, in particular those associated with twisted Lie superalgebras, are generally the most complex ones [1][2][3][4][5][53][54][55][56][57][58][59][60][61][62][63][64][65]. In fact, the classification of the reflection K-matrices for models associated with Lie superalgebras is not yet complete.…”

Section: (Although Its Hamiltonianmentioning

confidence: 99%

Reflection K-matrices for a nineteen vertex model with Uq[osp(2|2)
Vieira
¹
,
Santos
²

2017
Physics Letters A
2
0
3
0
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We derive the solutions of the boundary Yang-Baxter equation associated with a supersymmetric nineteen vertex model constructed from the three-dimensional representation of the twisted quantum affine Lie superalgebra U q [osp (2|2) (2) ]U q [C (2) (2) ]. We found three classes of solutions. The type I solution is characterized by three boundary free-parameters and all elements of the corresponding reflection K-matrix are different from zero. In the type II solution, the reflection K-matrix is even (every element of the K-matrix with an odd parity is null) and it has only one boundary free-parameter. Finally, the type III solution corresponds to a diagonal reflection K-matrix with two boundary free-parameters. The modelThis letter concerns with the reflection K-matrices of a supersymmetric nineteen vertex model introduced by Yang and Zhang in [1] (see also [2][3][4][5]). The Yang-Zhang R-matrix is constructed from a three-dimensional representation V of the twisted quantum affine Lie superalgebra(2) ], and the periodic algebraic Bethe Ansatz of this vertex model was performed in [6].Vertex models with underlying symmetries corresponding to Lie superalgebras are important in several fields of physics and mathematics. For instance, Z 2 -graded Lie superalgebras appear in the study of lattice models of strongly correlated electrons, such as the supersymmetric generalizations of the t-J model [7][8][9][10][11] and the Hubbard model [12,13], among others. The integrability of supersymmetric two-dimensional quantum chains had proved to be important as well in the AdS/CFT correspondence, either in the N = 4 super Yang-Mills side of the duality [14][15][16], or in the AdS 5 × S 5 string theory side [17]. Furthermore, these mathematical structures also are important in the construction of supersymmetric Hopf algebras and quantum groups [18][19][20][21] [30]. Considering now nonperiodic boundary conditions, the diagonal K-matrices for the ZFvm were first derived in [31] and the general Kmatrices were deduced in [32] and [33]; for the IKvm, the diagonal K-matrices were found in [34] and the general K-matrices were derived in [33] and [35]; besides, the coordinate Bethe Ansätze for both models were presented in [36], while their algebraic versions were performed in [37] (although the ZFvm had been considered before in [31] with the help of the fusion procedure [26]). Among the ZFvm and IKvm, other nineteen vertex models were discovered since then, for instance, the supersymmetric vertex models associated with the sl (2|1) and osp (2|1) Lie superalgebras, whose R-matrix was presented in [38] and the corresponding reflection K-matrices were obtained in [33]; for the Bethe Ansätze of these models, see [36,39]. Finally, other more complex nineteen vertex models were also discovered in the last decade − see, for instance, [40][41][42][43][44][45].The supersymmetric nineteen vertex model which we consider here is not included in the list above. The Rmatrix associated with this model was constructed in [1] and it can be wri...

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“…Later the homogeneous realization of simply laced affine Lie algebras at level one was given by I. Frenkel-Kac [12] and Segal [19]. Fermionic realizations were also constructed by I. Frenkel [10] and Kac-Peterson [16], and were generalized to arbitrary types by Feingold and I. Frenkel [9].…”

Section: Introductionmentioning

confidence: 99%

Realizations of Affine Lie Algebra $${A^{(1)}_1}$$ at Negative Levels

Dong¹,

Jing²

2014

Springer Proceedings in Mathematics &Amp; Statistics

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Classical affine algebras

Cited by 107 publications

References 6 publications

Locally supersymmetric σ-model with Wess-Zumino term in two dimensions and critical dimensions for strings

Locally supersymmetric σ-model with Wess-Zumino term in two dimensions and critical dimensions for strings

Reflection K-matrices for a nineteen vertex model with Uq[osp(2|2)
Vieira
¹
,
Santos
²

2017
Physics Letters A
2
0
3
0
View full text Add to dashboard Cite

Realizations of Affine Lie Algebra $${A^{(1)}_1}$$ at Negative Levels

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Classical affine algebras

Cited by 107 publications

References 6 publications

Locally supersymmetric σ-model with Wess-Zumino term in two dimensions and critical dimensions for strings

Locally supersymmetric σ-model with Wess-Zumino term in two dimensions and critical dimensions for strings

Reflection K-matrices for a nineteen vertex model with Uq[osp(2|2)Vieira1, Santos2 2017Physics Letters A2030View full textAdd to dashboardCite

Realizations of Affine Lie Algebra $${A^{(1)}_1}$$ at Negative Levels

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Product

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About

Reflection K-matrices for a nineteen vertex model with Uq[osp(2|2)
Vieira
¹
,
Santos
²

2017
Physics Letters A
2
0
3
0
View full text Add to dashboard Cite