38 research outputs found

### Minimization of the scalar Higgs potential in the Finite Supersymmetric Grand Unified Theory

Exact mathematical solution of the minimization conditions of scalar the
Higgs potential of the Finite Supersymmetric Grand Unification Theory is
proposed and extremal field configurations are found. Types of extrema are
investigated and masses of the new Higgs particles arisen after electroweak
symmetry breaking are derived analytically. The conditions for existing of
physically acceptable minimum are given. As it appears, this minimum is simple
generalization of the analogous solution in the Minimal Supersymmetric Standard
Model. Phenomenological consequences are discussed briefly.Comment: Latex, 18 pages, 1 postscript figure (included at the end

### An approach to solve Slavnov-Taylor identity in D4 N=1 supergravity

We consider a particular solution to Slavnov-Taylor identity in
four-dimensional supergravity. The consideration is performed for pure
supergravity, no matter superfields are included. The solution is obtained by
inserting dressing functions into ghost part of the classical action for
supergravity.As a consequence, physical part of the effective action is local
invariant with respect to diffeomorphism and structure groups of transformation
for dressed effective superfields of vielbein and spin connection.Comment: 6 pages, minor changes, to appear in Mod.Phys.Lett.

### QCD effective action with dressing functions - consistency checks in the perturbative regime

In a previous paper, we presented solution to the Slavnov--Taylor identity
for the QCD effective action, and argued that the action terms containing
(anti)ghost fields are unique. These terms have the same form as those in the
classical action, but the gluon and (anti)ghost effective fields are convoluted
with gluon and ghost dressing functions G_A and G_c, the latter containing
perturbative and nonperturbative effects (but not including the soliton-like
vacuum effects). In the present work we show how the perturbative QCD (pQCD)
can be incorporated into the framework of this action, and we present explicit
one-loop pQCD expressions for G_A and G_c. We then go on to check the
consistency of the obtained results by considering an antighost
Dyson--Schwinger equation (DSE). By solving the relations that result from the
Legendre transformation leading to the effective action, we obtain the
effective fields as power expansions of sources. We check explicitly that the
aforementioned one-loop functions G_A and G_c fulfil the antighost DSE at the
linear source level. We further explicitly check that these one-loop G_A and
G_c have the regularization-scale and momentum dependence consistent with the
antighost DSE at the quadratic source level. These checks suggest that the the
effective action with dressing functions represents a consistent framework for
treating QCD, at least at the one-loop level.Comment: 17 pages, revtex4; dimensional regularization used instead of
Pauli-Villars, the check of identity in the linear-in-sources Dyson-Schwinger
equation now includes the finite part; conclusions unchanged; to appear in
Phys.Rev.

### Difficulties of an Infrared Extension of Differential Renormalization

We investigate the possibility of generalizing differential renormalization
of D.Z.Freedman, K.Johnson and J.I.Latorre in an invariant fashion to theories
with infrared divergencies via an infrared $\tilde{R}$ operation.
Two-dimensional $\sigma$ models and the four-dimensional $\phi^4$ theory
diagrams with exceptional momenta are used as examples, while dimensional
renormalization serves as a test scheme for comparison. We write the basic
differential identities of the method simultaneously in co-ordinate and
momentum space, introducing two scales which remove ultraviolet and infrared
singularities. The consistent set of Fourier-transformation formulae is
derived. However, the values for tadpole-type Feynman integrals in higher
orders of perturbation theory prove to be ambiguous, depending on the order of
evaluation of the subgraphs. In two dimensions, even earlier than this
ambiguity manifests itself, renormalization-group calculations based on
infrared extension of differential renormalization lead to incorrect results.
We conclude that the extended differential renormalization procedure does not
perform the infrared $\tilde{R}$ operation in a self-consistent way, as the
original recipe does the ultraviolet $R$ operation.Comment: (minor changes have been made to make clear that no infrared problems
occur in the original ultraviolet procedure of [1]; subsection 2.1 has been
added to outline the ideas a simple example), 26 pages, LaTeX, JINR preprint
E2-92-538, Dubna (Dec.1992

### Towards the two-loop Lcc vertex in Landau gauge

We are interested in the structure of the Lcc vertex in the Yang-Mills
theory, where c is the ghost field and L the corresponding BRST auxiliary
field. This vertex can give us information on other vertices, and the possible
conformal structure of the theory should be reflected in the structure of this
vertex. There are five two-loop contributions to the Lcc vertex in the
Yang-Mills theory. We present here calculation of the first of the five
contributions. The calculation has been performed in the position space. One
main feature of the result is that it does not depend on any scale, ultraviolet
or infrared. The result is expressed in terms of logarithms and Davydychev
integral J(1,1,1) that are functions of the ratios of the intervals between
points of effective fields in the position space. To perform the calculation we
apply Gegenbauer polynomial technique and uniqueness method.Comment: 27 pp, 2 figures, Latex2e, revised version, to appear in IJMPA,
references added, comments on nonsupersymmetric case adde

### Further results for the two-loop Lcc vertex in the Landau gauge

In the previous paper hep-th/0604112 we calculated the first of the five
planar two-loop diagrams for the Lcc vertex of the general non-Abelian
Yang-Mills theory, the vertex which allows us in principle to obtain all other
vertices via the Slavnov-Taylor identity. The integrand of this first diagram
has a simple Lorentz structure. In this letter we present the result for the
second diagram, whose integrand has a complicated Lorentz structure. The
calculation is performed in the D-dimensional Euclidean position space. We
initially perform one of the two integrations in the position space and then
reduce the Lorentz structure to D-dimensional scalar single integrals. Some of
the latter are then calculated by the uniqueness method, others by the
Gegenbauer polynomial technique. The result is independent of the ultraviolet
and the infrared scale. It is expressed in terms of the squares of spacetime
intervals between points of the effective fields in the position space -- it
includes simple powers of these intervals, as well as logarithms and
polylogarithms thereof, with some of the latter appearing within the Davydychev
integral J(1,1,1). Concerning the rest of diagrams, we present the result for
the contributions correponding to third, fourth and fifth diagrams without
giving the details of calculation. The full result for the Lcc correlator of
the effective action at the planar two-loop level is written explicitly for
maximally supersymmetric Yang-Mills theory.Comment: 29 pages, 1 figure, minor changes; three references added, one new
paragraph in Introduction added, Note Added is extended; to appear in JHE

### Comment on the ``$\theta$-term renormalization in the (2+1)-dimensional $CP^{N-1}$ model with $\theta$ term''

It is found that the recently published first coefficient of nonzero
$\beta$-function for the Chern-Simons term in the $1/N$ expansion of the
$CP^{N-1}$ model is untrue numerically. The correct result is given. The main
conclusions of Park's paper are not changed.Comment: 3 pages, LATE

### An approach to solve Slavnov-Taylor identities in nonsupersymmetric non-Abelian gauge theories

We present a way to solve Slavnov--Taylor identities in a general
nonsupersymmetric theory. The solution can be parametrized by a limited number
of functions of spacetime coordinates, so that all the effective fields are
dressed by these functions via integral convolution. The solution restricts the
ghost part of the effective action and gives predictions for the physical part
of the effective action.Comment: revised version, section 3 is enlarged, 24 pages, Latex2e, no
figures, version accepted by Phys. Rev.