Multiple integral formulae for the scalar product of on-shell and off-shell Bethe vectors in SU(3)-invariant models

Abstract

We study the scalar product S_{l,m} between an on-shell and an off-shell Bethe state in models with SU(3)-invariance, where l and m denote the cardinalities of the two sets of Bethe roots. We construct recursion relations relating S_{l,m} to scalar products of smaller dimension, namely S_{l-1,m} and S_{l,m-1}. Solving these recursion relations we obtain new multiple integral expressions for S_{l,m}, whose integrands are (l+m) \times (l+m) determinants, and closely related to the Slavnov determinant expression for the SU(2) scalar product.

19 pages, 5 figures, a reference added in v2

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• Comments on World-Sheet Form Factors in AdS/CFT
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• Form factors of the half-infinite XXZ spin chain with a triangular boundary
• Asymptotic behaviour of two-point functions in multi-species models
• Nested Algebraic Bethe Ansatz in integrable models: recent results
• On correlation functions in the coordinate and the algebraic Bethe ansatz