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.

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

References in corpus (7)

• On AdS_5 x S^5 String S-matrix
• Classical r-matrix of the su(2|2) SYM spin-chain
• 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
• Multiple Actions of the Monodromy Matrix in $\mathfrak{gl}(2|1)$-Invariant Integrable Models
• Form factors of the monodromy matrix entries in gl(2|1)-invariant integrable models
• Generating Series for Nested Bethe Vectors

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