Yangians in Deformed Super Yang-Mills Theories

TL;DR

This paper investigates the Yangian algebra structure in deformed N=4 super Yang-Mills theories, demonstrating the persistence of integrability through twisted coproducts in certain residual symmetries.

Contribution

It analyzes the Yangian algebra in deformed super Yang-Mills theories, revealing how twisted coproducts relate to residual symmetries and integrability.

Findings

Retained integrable structure in deformed theories.

Computed twisted coproducts for residual symmetries.

Full Yangian structure persists with twisted coproducts.

Abstract

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|1)xU(1)xU(1). 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)xU(1)xU(1)xU(1) and SU(2|1)xU(1)xU(1) as residual symmetries of SU(2,2|1)xU(1)xU(1). 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.