Current presentation for the double super-Yangian $DY(\mathfrak{gl}(m|n))$ and Bethe vectors

Abstract

We find Bethe vectors for quantum integrable models associated with the supersymmetric Yangians $Y(\mathfrak{gl}(m|n)$ in terms of the current generators of the Yangian double $DY(\mathfrak{gl}(m|n))$. More specifically, we use the method of projections onto intersections of different type Borel subalgebras in this infinite dimensional algebra to construct the Bethe vectors. Calculating these projection the supersymmetric Bethe vectors can be expressed through matrix elements of the universal monodromy matrix elements. Using two different but isomorphic current realizations of the Yangian double $DY(\mathfrak{gl}(m|n))$ we obtain two different presentations for the Bethe vectors. These Bethe vectors are also shown to obey some recursion relations which prove their equivalence.

arXiv comment61 pages; some typos corrected; title changed to make it more precise and distinguish it from a previous publication

References in corpus (19)

• The Bethe-Ansatz for N=4 Super Yang-Mills
• Quantum Inverse Scattering Method and Correlation Functions
• Bethe Ansatz for Quantum Strings
• The Zamolodchikov-Faddeev Algebra for AdS_5 x S^5 Superstring
• On AdS_5 x S^5 String S-matrix
• Nested Bethe ansatz for "all" closed spin chains
• Bethe vectors of GL(3)-invariant integrable models
• Combinatorial Formulae for Nested Bethe Vectors
• Jackson Integral Representations for Solutions to the Quantized Knizhnik-Zamolodchikov Equation
• Classical r-matrix of the su(2|2) SYM spin-chain
• Form factors in SU(3)-invariant integrable models
• Drinfeld second realization of the quantum affine superalgebras of $D^{(1)}(2,1;x)$ via the Weyl groupoid
• On the Scattering Phase for AdS_5 x S^5 Strings
• Bethe Vectors of Quantum Integrable Models with GL(3) Trigonometric $R$-Matrix
• Multiple Actions of the Monodromy Matrix in $\mathfrak{gl}(2|1)$-Invariant Integrable Models
• Bethe Ansatz for the Universal Weight Function
• Form factors of the monodromy matrix entries in gl(2|1)-invariant integrable models
• Super Yangian Double and its Central Extension
• Generating Series for Nested Bethe Vectors

Cited by in corpus (23)

• Scalar products of Bethe vectors in the models with $\mathfrak{gl}(m|n)$ symmetry
• Why scalar products in the algebraic Bethe ansatz have determinant representation
• On Bethe vectors in ${\mathfrak{gl}}_3$-invariant integrable models
• On factorized overlaps: Algebraic Bethe Ansatz, twists, and Separation of Variables
• Liouville reflection operator, affine Yangian and Bethe ansatz
• On exact overlaps for $\mathfrak{gl}(N)$ symmetric spin chains
• Norm of Bethe vectors in models with $\mathfrak{gl}(m|n)$ symmetry
• New Compact Construction of Eigenstates for Supersymmetric Spin Chains
• On Scalar Products in Higher Rank Quantum Separation of Variables
• Form factors of local operators in supersymmetric quantum integrable models
• Separation of variables bases for integrable $g{l}_{\mathcal{M}|\mathcal{N}}$ and Hubbard models
• Introduction to the nested algebraic Bethe ansatz
• Scalar products and norm of Bethe vectors for integrable models based on $U_q({\widehat{\mathfrak{gl}}}_n)$
• Bethe vectors for orthogonal integrable models
• New symmetries of $\mathfrak{gl}(N)$-invariant Bethe vectors
• Actions of the monodromy matrix elements onto $\mathfrak{gl}(m|n)$-invariant Bethe vectors
• Nested Algebraic Bethe Ansatz in integrable models: recent results
• Gauss Coordinates vs Currents for the Yangian Doubles of the Classical Types
• Recurrence relations for off-shell Bethe vectors in trigonometric integrable models
• Scalar products and norm of Bethe vectors in ${\mathfrak{o}}_{2n+1}$ invariant integrable models
• Algebraic Bethe ansatz for ${\mathfrak{o}}_{2n+1}$-invariant integrable models
• On the R-matrix realization of the quantum loop algebra. The case of $U_q(D_n^{(2)})$
• Multiple commutation relations of the quantum affine algebra $U_q({\widehat{\mathfrak{gl}}}_N)$, nested Bethe vector and the Gelfand-Tsetlin basis