On factorising twists in AdS_3 and AdS_2

TL;DR

This paper investigates factorising twists of massless AdS_3 and AdS_2 integrable R-matrices, deriving them from the universal R-matrix of the gl(1|1) Yangian double, and explores their applications in form factors and scalar products.

Contribution

It introduces a method to derive factorising twists from the universal R-matrix of the gl(1|1) Yangian double for AdS_3 and AdS_2, and applies this to compute scalar products and form factors.

Findings

Derived factorising twists from the universal R-matrix.

Connected twists to scalar product computations.

Extended the construction to free fermions and massless AdS_2 R-matrix.

Abstract

In this paper we study factorising twists of the massless AdS_3 and AdS_2 integrable R-matrices, and explore the programme of analysis of form factors which Maillet et al developed for ordinary spin-chains. 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 AdS_2 quantum R-matrix from the Yangian universal R-matrix, and compute a peculiar factorising twist for this case as well.