Trigonometric osp(1|2) Gaudin model

The integrable structure of the two-dimensional superconformal field theory is considered. The classical counterpart of our constructions is based on the osp(1|2) super-KdV hierarchy. The quantum version of the monodromy matrix associated with the linear problem for the corresponding L-operator is introduced. Using the explicit form of the irreducible representations of osp q (1|2), the so-called "fusion relations" for the transfer matrices considered in different representations of osp q (1|2) are obtained. The possible integrable perturbations of the model (primary operators, commuting with integrals of motion) are classified and the relation with the supersymmetric osp(1|2) Toda field theory is discussed.

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“…where R ss is the trigonometric solution of the corresponding Yang-Baxter equation [16] which acts in the space π s (λ) ⊗ π s (µ).…”

Section: Quantum Monodromy Matrix and Fusion Relationsmentioning

confidence: 99%

Integrable structure of superconformal field theory and quantum super-KdV theory

Kulish

Zeitlin

2004

Physics Letters B

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“…A generalization of these results to all cases when skew-symmetric r-matrix satisfies the classical Yang-Baxter equation [22] was relatively straightforward [23,24]. Therefore, considerable attention has been devoted to Gaudin models corresponding to the classical r-matrices of simple Lie algebras [25][26][27] and Lie superalgebras [28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 98%

Algebraic Bethe ansatz for the XXX chain with triangular boundaries and Gaudin model

2014

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We implement fully the algebraic Bethe ansatz for the XXX Heisenberg spin chain in the case when both boundary matrices can be brought to the upper-triangular form. We define the Bethe vectors which yield the strikingly simple expression for the off shell action of the transfer matrix, deriving the spectrum and the relevant Bethe equations. We explore further these results by obtaining the off shell action of the generating function of the Gaudin Hamiltonians on the corresponding Bethe vectors through the so-called quasi-classical limit. Moreover, this action is as simple as it could possibly be, yielding the spectrum and the Bethe equations of the Gaudin model.

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“…A generalisation of these results to all cases when skew-symmetric r-matrix satisfies the classical Yang-Baxter equation [4] was relatively straightforward [5,6]. Therefore, considerable attention has been devoted to Gaudin models corresponding to the classical r-matrices of simple Lie algebras [7][8][9][10][11][12] and Lie superalgebras [13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Algebraic Bethe ansatz for thesℓ(2)Gaudin model with boundary

et al. 2015

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Following Sklyanin's proposal in the periodic case, we derive the generating function of the Gaudin Hamiltonians with boundary terms. Our derivation is based on the quasi-classical expansion of the linear combination of the transfer matrix of the XXX Heisenberg spin chain and the central element, the so-called Sklyanin determinant. The corresponding Gaudin Hamiltonians with boundary terms are obtained as the residues of the generating function. By defining the appropriate Bethe vectors which yield strikingly simple off shell action of the generating function, we fully implement the algebraic Bethe ansatz, obtaining the spectrum of the generating function and the corresponding Bethe equations. (E. Ragoucy), isalom@ipb.ac.rs (I. Salom).

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Trigonometric osp(1|2) Gaudin model

Cited by 28 publications

References 42 publications

Integrable structure of superconformal field theory and quantum super-KdV theory

Integrable structure of superconformal field theory and quantum super-KdV theory

Algebraic Bethe ansatz for the XXX chain with triangular boundaries and Gaudin model

Algebraic Bethe ansatz for thesℓ(2)Gaudin model with boundary

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