Yangians in deformed super Yang-Mills theories

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)×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)×U(1) 3 and SU(2|1)×U(1) 2 as residual symmetries of SU(2, 2|1)×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.

Untwisting the symmetries of β-deformed Super-Yang-Mills

“…It is natural to expect that the integrability of the real-β-deformed theory will be explained by a suitable deformation of this Yangian algebra. It was indeed shown in [12] that some closed subsectors of it do enjoy a twisted Yangian symmetry, resonating well with the results of [13] on the twisted R-matrix.…”

“…Indeed, for the N = 4 SYM the Yangian of psu(2, 2|4) underlies its integrability. Twisted Yangian algebra has been identified in [12] as the symmetry of some subsectors of the real-βdeformed SYM. We would now like to promote this discussion to a full theory, taking into account the nonlinearities of the symmetries.…”

Bilocal phase operators inβ-deformed super Yang-Mills

“…Marginal deformations of conformally invariant supersymmetric gauge theories were first systematically studied by Leigh and Strassler [17], and have subsequently been analyzed extensively both perturbatively and at strong coupling in [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33] just to mention a few.…”

“…Of important properties of the star product we mention associativity, which is a consequence of additivity of the flavor charges, and noncommutativity, the latter being obvious from the definition (27).…”

Yangians,S-matrices and AdS/CFT

“…In [107], a large degeneracy of states in the psu(1, 1|2) sector has been explained by finding nonlocal charges related to the loop-algebra of the su(2) automorphism of psu(1, 1|2). Further references include [112][113][114][115][116][117][118].…”