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|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.Comment: 17 page

Conformal invariance of the planar beta-deformed N=4 SYM theory requires beta real

We study the \cal{N}=1 SU(N) SYM theory which is a marginal deformation of the \cal{N}=4 theory, with a complex deformation parameter \beta. We consider the large N limit and study perturbatively the conformal invariance condition. We find that finiteness requires reality of the deformation parameter \beta.Comment: LaTex, 15 pages, 7 figure

Real versus complex beta-deformation of the N=4 planar super Yang-Mills theory

This is a sequel of our paper hep-th/0606125 in which we have studied the {\cal N}=1 SU(N) SYM theory obtained as a marginal deformation of the {\cal N}=4 theory, with a complex deformation parameter \beta and in the planar limit. There we have addressed the issue of conformal invariance imposing the theory to be finite and we have found that finiteness requires reality of the deformation parameter \beta. In this paper we relax the finiteness request and look for a theory that in the planar limit has vanishing beta functions. We perform explicit calculations up to five loop order: we find that the conditions of beta function vanishing can be achieved with a complex deformation parameter, but the theory is not finite and the result depends on the arbitrary choice of the subtraction procedure. Therefore, while the finiteness condition leads to a scheme independent result, so that the conformal invariant theory with a real deformation is physically well defined, the condition of vanishing beta function leads to a result which is scheme dependent and therefore of unclear significance. In order to show that these findings are not an artefact of dimensional regularization, we confirm our results within the differential renormalization approach.Comment: 18 pages, 7 figures; v2: one reference added; v3: JHEP published versio

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Gluon Scattering in Deformed N=4 SYM

We consider gluon and gluino scattering amplitudes in large N beta-deformed N=4 SYM with real beta. A direct inspection of the planar diagrams shows that the scattering amplitudes to all orders in perturbation theory are the same as in the undeformed N=4 SYM theory. Using the dual sigma-model description, we find the same equality at strong coupling to all orders in the sigma-model loop expansion. Finally, we show that the same analysis holds for gluon scattering amplitudes in a three-parameter deformation of planar N=4 SYM that breaks all the supersymmetry.Comment: 10 pages; a comment and references adde

On the non-planar beta-deformed N=4 super-Yang-Mills theory

The beta-deformation is one of the two superconformal deformations of the N=4 super-Yang-Mills theory. At the planar level it shares all of its properties except for supersymmetry, which is broken to the minimal amount. The tree-level amplitudes of this theory exhibit new features which depart from the commonly assumed properties of gauge theories with fields in the adjoint representation. We analyze in detail complete one-loop amplitudes and a nonplanar two-loop amplitude of this theory and show that, despite having only N=1 supersymmetry, two-loop amplitudes have a further-improved ultraviolet behavior. This phenomenon is a counterpart of a similar improvement previously observed in the double-trace amplitude of the N=4 super-Yang-Mills theory at three and four loop order and points to the existence of additional structure in both the deformed and undeformed theories.Comment: 39 pages, 8 figure

Notes on beta-deformations of the pure spinor superstring in AdS(5) x S(5)

We study the properties of the vertex operator for the beta-deformation of the superstring in AdS(5) x S(5) in the pure spinor formalism. We discuss the action of supersymmetry on the infinitesimal beta-deformation, the application of the homological perturbation theory, and the relation between the worldsheet description and the spacetime supergravity description.Comment: LaTeX, 74pp

Field Representations of Vector Supersymmetry

We study some field representations of vector supersymmetry with superspin Y=0 and Y=1/2 and nonvanishing central charges. For Y=0, we present two multiplets composed of four spinor fields, two even and two odd, and we provide a free action for them. The main differences between these two multiplets are the way the central charge operators act and the compatibility with the Majorana reality condition on the spinors. One of the two is related to a previously studied spinning particle model. For Y=1/2, we present a multiplet composed of one even scalar, one odd vector and one even selfdual two-form, which is a truncation of a known representation of the tensor supersymmetry algebra in Euclidean spacetime. We discuss its rotation to Minkowski spacetime and provide a set of dynamical equations for it, which are however not derived from a Lagrangian. We develop a superspace formalism for vector supersymmetry with central charges and we derive our multiplets by superspace techniques. Finally, we discuss some representations with vanishing central charges.Comment: 37 page

On the all-order perturbative finiteness of the deformed N=4 SYM theory

We prove that the chiral propagator of the deformed N=4 SYM theory can be made finite to all orders in perturbation theory for any complex value of the deformation parameter. For any such value the set of finite deformed theories can be parametrized by a whole complex function of the coupling constant g. We reveal a new protection mechanism for chiral operators of dimension three. These are obtained by differentiating the Lagrangian with respect to the independent coupling constants. A particular combination of them is a CPO involving only chiral matter. Its all-order form is derived directly from the finiteness condition. The procedure is confirmed perturbatively through order g^6.Comment: LaTeX, 28 pages, 5 figure