10 research outputs found
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
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 {\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
IFUM–892–FT Bicocca-FT-06-14
This is a sequel of our paper hep-th/0606125 in which we have studied the N = 1 SU(N) SYM theory obtained as a marginal deformation of the N = 4 theory, with a complex deformation parameter β 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 β. 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