Yangians in deformed super Yang-Mills theories

Abstract We discuss the integrability structure of deformed, four-dimensional = 4 super Yang-Mills theories using Yangians. We employ a recent procedure by Beisert and Roiban that generalizes the beta deformation of Lunin and Maldacena to produce = 1 superconformal gauge theories, which have the superalgebra SU (2,2|1)\times U $(1)^2$ 2 . The deformed theories, including those with the more general twist, were shown to have retained their integrable structure. Here we examine the Yangian algebra of these deformed theories. In a five field subsector, we compute the two cases of SU(2) \times U(1) 3 and SU(2|1) \times U(1) 2 as residual symmetries of SU (2,2|1)\times U(1) 2 . We compute a twisted coproduct for these theories, and show that only for the residual symmetry do we retain the standard coproduct. The twisted coproduct thus provides a method for symmetry breaking. However, the full Yangian structure of SU(2|3) is manifest in our subsector, albeit with twisted coproducts, and provides for the integrability of the theory