48 research outputs found
Bosonic String and String Field Theory: a solution using Ultradistributions of Exponential Type
In this paper we show that Ultradistributions of Exponential Type (UET) are
appropriate for the description in a consistent way string and string field
theories. A new Lagrangian for the closed string is obtained and shown to be
equivalent to Nambu-Goto's Lagrangian. We also show that the string field is a
linear superposition of UET of compact support CUET). We evaluate the
propagator for the string field, and calculate the convolution of two of them.Comment: 30 page
Dimensional Reduction applied to QCD at three loops
Dimensional Reduction is applied to \qcd{} in order to compute various
renormalization constants in the \drbar{} scheme at higher orders in
perturbation theory. In particular, the function and the anomalous
dimension of the quark masses are derived to three-loop order. Special emphasis
is put on the proper treatment of the so-called -scalars and the
additional couplings which have to be considered.Comment: 13 pages, minor changes, references adde
Higher loop corrections to a Schwinger--Dyson equation
We consider the effects of higherloop corrections to a Schwinger--Dyson
equations for propagators. This is made possible by the efficiency of the
methods we developed in preceding works, still using the supersymmetric
Wess--Zumino model as a laboratory. We obtain the dominant contributions of the
three and four loop primitive divergences at high order in perturbation theory,
without the need for their full evaluations. Our main conclusion is that the
asymptotic behavior of the perturbative series of the renormalization function
remains unchanged, and we conjecture that this will remain the case for all
finite order corrections.Comment: 12 pages, 2 imbedded TiKZ pictures. A few clarifications matching the
published versio
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
An Algorithm to Construct Groebner Bases for Solving Integration by Parts Relations
This paper is a detailed description of an algorithm based on a generalized
Buchberger algorithm for constructing Groebner-type bases associated with
polynomials of shift operators. The algorithm is used for calculating Feynman
integrals and has proven itself efficient in several complicated cases.Comment: LaTeX, 9 page
Four-loop beta function and mass anomalous dimension in Dimensional Reduction
Within the framework of QCD we compute renormalization constants for the
strong coupling and the quark masses to four-loop order. We apply the DR-bar
scheme and put special emphasis on the additional couplings which have to be
taken into account. This concerns the epsilon-scalar--quark Yukawa coupling as
well as the vertex containing four epsilon-scalars. For a supersymmetric Yang
Mills theory, we find, in contrast to a previous claim, that the evanescent
Yukawa coupling equals the strong coupling constant through three loops as
required by supersymmetry.Comment: 15 pages, fixed typo in Eq. (18
An easy way to solve two-loop vertex integrals
Negative dimensional integration is a step further dimensional regularization
ideas. In this approach, based on the principle of analytic continuation,
Feynman integrals are polynomial ones and for this reason very simple to
handle, contrary to the usual parametric ones. The result of the integral
worked out in must be analytically continued again --- of course --- to
real physical world, , and this step presents no difficulties. We consider
four two-loop three-point vertex diagrams with arbitrary exponents of
propagators and dimension. These original results give the correct well-known
particular cases where the exponents of propagators are equal to unity.Comment: 13 pages, LaTeX, 4 figures, misprints correcte
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
Dynamics near the critical point: the hot renormalization group in quantum field theory
The perturbative approach to the description of long wavelength excitations
at high temperature breaks down near the critical point of a second order phase
transition. We study the \emph{dynamics} of these excitations in a relativistic
scalar field theory at and near the critical point via a renormalization group
approach at high temperature and an expansion in
space-time dimensions. The long wavelength physics is determined by a
non-trivial fixed point of the renormalization group. At the critical point we
find that the dispersion relation and width of quasiparticles of momentum
is and respectively, the
group velocity of quasiparticles vanishes in the long
wavelength limit at the critical point. Away from the critical point for
we find and
with
the finite temperature correlation length . The
new \emph{dynamical} exponent results from anisotropic renormalization in
the spatial and time directions. For a theory with O(N) symmetry we find . Critical slowing down,
i.e, a vanishing width in the long-wavelength limit, and the validity of the
quasiparticle picture emerge naturally from this analysis.Comment: Discussion on new dynamical universality class. To appear in Phys.
Rev.
Differential Equations for Definition and Evaluation of Feynman Integrals
It is shown that every Feynman integral can be interpreted as Green function
of some linear differential operator with constant coefficients. This
definition is equivalent to usual one but needs no regularization and
application of -operation. It is argued that presented formalism is
convenient for practical calculations of Feynman integrals.Comment: pages, LaTEX, MSU-PHYS-HEP-Lu2/9