The Nested Off-shell Bethe ansatz and O(N) Matrix Difference Equations

Abstract

A system of O(N)-matrix difference equations is solved by means of the off-shell version of the nested algebraic Bethe ansatz. In the nesting process a new object, the $\Pi$-matrix, is introduced to overcome the complexities of the O(N) group structure. The proof of the main theorem is presented in detail. In particular, the cancellation of all unwanted terms is shown explicitly. The highest weight property of the solutions is proved.

This paper contains detailed proofs and pictures which were shortened or skipped in JPA45 (2012) 055207, 40 pages

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Cited by in corpus (5)

• Space-time S-matrix and Flux tube S-matrix II. Extracting and Matching Data
• Exact form factors of the O(N) $\sigma$-model
• Nested algebraic Bethe ansatz for deformed orthogonal and symplectic spin chains
• Bethe Ansatz and exact form factors of the O(N) Gross Neveu-model
• Scalar products and norm of Bethe vectors in ${\mathfrak{o}}_{2n+1}$ invariant integrable models