Yangians in deformed super Yang-Mills theories

We discuss the integrability structure of deformed, four-dimensional N = 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 N = 1 superconformal gauge theories, which have the superalgebra SU(2,2 vertical bar 1) x U(1)(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) x U(1)(3) and SU(2 vertical bar 1) x U(1)(2) as residual symmetries of SU(2, 2 vertical bar 1) x 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 vertical bar 3) is manifest in our subsector, albeit with twisted coproducts, and provides for the integrability of the theory.