Abstract We consider the rational six-vertex model on anL×Llattice with domain wall boundary conditions and restrictNparallel-line rapidities,N≤L/2, to satisfy length-LXXX

\mathrm{spin}-\frac{1}{2}

chain Bethe equations. We show that the partition function is an (L− 2N)- parameter extension of Slavnov’s scalar product of a Bethe eigenstate and a generic state, withNmagnons each, on a length-LXXX

\mathrm{spin}-\frac{1}{2}

chain. Decoupling the extra parameters, we obtain a third determinant expression for the scalar product, where the first is due to Slavnov [1], and the second is due to Kostov and Matsuo [2]. We show that the new determinant is Casoratian, and consequently that tree-level

\mathcal{N}=4

SYM structure constants that are known to be determinants, remain determinants at 1-loop level.

DOI: 10.1007/jhep10(2012)096

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Abstract We consider the rational six-vertex model on anL×Llattice with domain wall boundary conditions and restrictNparallel-line rapidities,N≤L/2, to satisfy length-LXXX

\mathrm{spin}-\frac{1}{2}

\mathrm{spin}-\frac{1}{2}

\mathcal{N}=4

SYM structure constants that are known to be determinants, remain determinants at 1-loop level.