On factorising twists in AdS_3 and AdS_2

Abstract

In this paper we study factorising twists of the massless AdS3 and AdS2 integrable R-matrices, and explore the programme of analysis of form factors which Maillet et al developed for ordinary spinchains. We derive the factorising twists from the universal R-matrix of the gl(1|1) Yangian double, and discuss the RTT relations for the two-and three-site monodromy matrix. We show how the twist can be used to compute a simple scalar product. We then implement our construction in the language of free fermions. Finally, we show how to obtain the massless AdS2 quantum R-matrix from the Yangian universal R-matrix, and compute a peculiar factorising twist for this case as well.