Fusion for AdS/CFT boundary S-matrices

Abstract

We propose a fusion formula for AdS/CFT worldsheet boundary S-matrices. We show that, starting from the fundamental Y = 0 boundary S-matrix, this formula correctly reproduces the two-particle bound-state boundary S-matrices.

A tale of two Bethe ansätze

“…where ξ + is another arbitrary boundary parameter. The fused K − -matrix is given by (following [17])…”

“…For the ZF model, the construction of the Bethe vectors of the single and double-row transfer matrices can be performed in two different ways. The first one is by means of the fusion technique [5,6,7,8,9,10,11,12,13,14,15,16,17], where the auxiliary space is still 2-dimensional, and therefore the Bethe vectors are obtained similarly to the six-vertex model case. We shall refer to these as fusion-Bethe vectors.…”

“…In this section we recall some basic ingredients of the fusion technique, by means of which we can construct integrable generalizations of the fundamental six-vertex model, for both single-row [5][6][7][8][9][10][11][12][13][14] and double-row [15][16][17] transfer matrices.…”