Nested Bethe ansatz for "all" closed spin chains

Abstract

We present in an unified and detailed way the Nested Bethe Ansatz for closed spin chains based on Y(gl(n)), Y(gl(m|n)), U_q(gl(n)) or U_q(gl(m|n)) (super)algebras, with arbitrary representations (i.e. `spins') on each site of the chain. In particular, the case of indecomposable representations of superalgebras is studied. The construction extends and unifies the results already obtained for spin chains based on Y(gl(n)) or U_q(gl(n)) and for some particular super-spin chains. We give the Bethe equations and the form of the Bethe vectors. The case of gl(2|1), gl(2|2$ and gl(4|4) superalgebras (that are related to AdS/CFT correspondence) is also detailed.

30 pages; New section on indecomposable representations added and the case of gl(2|1), gl(2|2) and gl(4|4) superalgebras (that are related to AdS/CFT correspondence) is also detailed

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• The S-matrix algebra of the AdS2 X S2 superstring
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• New Compact Construction of Eigenstates for Supersymmetric Spin Chains
• Gaudin models for gl(m|n)
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• Form factors of local operators in supersymmetric quantum integrable models
• Complete spectrum of quantum integrable lattice models associated to ${\mathcal{U}}_q(\widehat{g{l}_n})$ by separation of variables
• Solutions of ${\mathfrak{gl}}_{m|n}$ XXX Bethe ansatz equation and rational difference operators
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• Scalar products and norm of Bethe vectors for integrable models based on $U_q({\widehat{\mathfrak{gl}}}_n)$
• New symmetries of $\mathfrak{gl}(N)$-invariant Bethe vectors
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• Supersymmetric extension of qKZ-Ruijsenaars correspondence
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• Folding QQ-relations and transfer matrix eigenvalues: towards a unified approach to Bethe ansatz for super spin chains
• Completeness of Bethe ansatz for Gaudin models associated with gl(1|1)
• On Bethe eigenvectors and higher transfer matrices for supersymmetric spin chains
• On factorizing $F$-matrices in $Y(s{l}_n)$ and $U_q(\widehat{s{l}_n})$ spin chains
• On correlation functions in the coordinate and the algebraic Bethe ansatz
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• Flag Integrable Models and Generalized Graded Algebras
• The Dynamical equations for $\mathfrak{gl}(n|m)$
• Momentum Evolution Numerics of an Impurity in a Quantum Quench