## 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.

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 Friday, September 9, 2011