40 research outputs found
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