The Bound State $S$-matrix of the Deformed Hubbard Chain

Marius de Leeuw, Takuya Matsumoto, Vidas Regelskis

Abstract

In this work we use the q-oscillator formalism to construct the atypical (short) supersymmetric representations of the centrally extended ${\mathcal{U}}_q(\mathfrak{su}(2|2))$ algebra. We then determine the S-matrix describing the scattering of arbitrary bound states. The crucial ingredient in this derivation is the affine extension of the aforementioned algebra.

Keywords: Quantum affine algebra, $q$-oscillator formalism, Hubbard Chain, $S$-matrix, AdS/CFT correspondence.