Paper detail

Partial domain wall partition functions

We consider six-vertex model configurations on an n-by-N lattice, n =< N, that satisfy a variation on domain wall boundary conditions that we define and call &#34;partial domain wall boundary conditions&#34;. We obtain two expressions for the corresponding &#34;partial domain wall partition function&#34;, as an (N-by-N)-determinant and as an (n-by-n)-determinant. The latter was first obtained by I Kostov. We show that the two determinants are equal, as expected from the fact that they are partition functions of the same object, that each is a discrete KP tau-function, and, recalling that these determinants represent tree-level structure constants in N=4 SYM, we show that introducing 1-loop corrections, as proposed by N Gromov and P Vieira, preserves the determinant structure.