20 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
OC09.04: Crownârump length and abdominal circumference discrepancy as early predictors of late adverse pregnancy outcome in monochorionic diamniotic pregnancies
n/
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
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
Factorization of Seiberg-Witten Curves with Fundamental Matter
We present an explicit construction of the factorization of Seiberg-Witten
curves for N=2 theory with fundamental flavors. We first rederive the exact
results for the case of complete factorization, and subsequently derive new
results for the case with breaking of gauge symmetry U(Nc) to U(N1)xU(N2). We
also show that integrality of periods is necessary and sufficient for
factorization in the case of general gauge symmetry breaking. Finally, we
briefly comment on the relevance of these results for the structure of N=1
vacua.Comment: 24 pages, 2 figure
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
Four-loop anomalous dimensions in Leigh-Strassler deformations
We determine the scalar part of the four-loop chiral dilatation operator for
Leigh-Strassler deformations of N=4 super Yang-Mills. This is sufficient to
find the four-loop anomalous dimensions for operators in closed scalar
subsectors. This includes the SU(2) subsector of the (complex)
beta-deformation, where we explicitly compute the anomalous dimension for
operators with a single impurity. It also includes the "3-string null"
operators of the cubic Leigh-Strassler deformation. Our four-loop results show
that the rational part of the anomalous dimension is consistent with a
conjecture made in arXiv:1108.1583 based on the three-loop result of
arXiv:1008.3351 and the N=4 magnon dispersion relation. Here we find additional
zeta(3) terms.Comment: Latex, feynmp, 21 page
On {\cal N}=1 exact superpotentials from U(N) matrix models
In this letter we compute the exact effective superpotential of {\cal N}=1
U(N) supersymmetric gauge theories with N_f fundamental flavors and an
arbitrary tree-level polynomial superpotential for the adjoint Higgs field. We
use the matrix model approach in the maximally confinig phase. When restricted
to the case of a tree-level even polynomial superpotential, our computation
reproduces the known result of the SU(N) theory.Comment: 15 pages, LaTe
Supergraphs and the cubic Leigh-Strassler model
We discuss supergraphs and their relation to "chiral functions" in N=4 Super
Yang-Mills. Based on the magnon dispersion relation and an explicit three-loop
result of Sieg's we make an all loop conjecture for the rational contributions
of certain classes of supergraphs. We then apply superspace techniques to the
"cubic" branch of Leigh-Strassler N=1 superconformal theories. We show that
there are order 2^L/L single trace operators of length L which have zero
anomalous dimensions to all loop order in the planar limit. We then compute the
anomalous dimensions for another class of single trace operators we call
one-pair states. Using the conjecture we can find a simple expression for the
rational part of the anomalous dimension which we argue is valid at least up to
and including five-loop order. Based on an explicit computation we can compute
the anomalous dimension for these operators to four loops.Comment: 22 pages; v2: Conjecture modified to apply only for the rational part
of the chiral functions. Typos fixed. Minor modification
Nonanticommutative U(1) SYM theories: Renormalization, fixed points and infrared stability
Renormalizable nonanticommutative SYM theories with chiral matter in the
adjoint representation of the gauge group have been recently constructed in
[arXiv:0901.3094]. In the present paper we focus on the U*(1) case with matter
interacting through a cubic superpotential. For a single flavor, in a
superspace setup and manifest background covariant approach we perform the
complete one-loop renormalization and compute the beta-functions for all
couplings appearing in the action. We then generalize the calculation to the
case of SU(3) flavor matter with a cubic superpotential viewed as a nontrivial
NAC generalization of the ordinary abelian N=4 SYM and its marginal
deformations. We find that, as in the ordinary commutative case, the NAC N=4
theory is one-loop finite. We provide general arguments in support of all-loop
finiteness. Instead, deforming the superpotential by marginal operators gives
rise to beta-functions which are in general non-vanishing. We study the
spectrum of fixed points and the RG flows. We find that nonanticommutativity
always makes the fixed points unstable.Comment: 1+30 pages, 5 figure