2,014 research outputs found
Conformal Invariance = Finiteness and Beta Deformed N=4 SYM Theory
We claim that if by a choice of the couplings the theory can be made
conformally invariant (vanishing of the beta functions) it is automatically
finite and vice versa. This is demonstrated by explicit example in
supersymmetric gauge theory. The formalism is then applied to the beta deformed
SYM theory and it is shown that the requirement of conformal
invariance = finiteness can be achieved for any complex parameter of
deformations.Comment: 15 pages, Latex, 1 figure axodraw styl
Effective Gravitational Field of Black Holes
The problem of interpretation of the \hbar^0-order part of radiative
corrections to the effective gravitational field is considered. It is shown
that variations of the Feynman parameter in gauge conditions fixing the general
covariance are equivalent to spacetime diffeomorphisms. This result is proved
for arbitrary gauge conditions at the one-loop order. It implies that the
gravitational radiative corrections of the order \hbar^0 to the spacetime
metric can be physically interpreted in a purely classical manner. As an
example, the effective gravitational field of a black hole is calculated in the
first post-Newtonian approximation, and the secular precession of a test
particle orbit in this field is determined.Comment: 8 pages, LaTeX, 1 eps figure. Proof of the theorem and typos
correcte
Two-logarithm matrix model with an external field
We investigate the two-logarithm matrix model with the potential
related to an exactly solvable
Kazakov-Migdal model. In the proper normalization, using Virasoro constraints,
we prove the equivalence of this model and the Kontsevich-Penner matrix model
and construct the 1/N-expansion solution of this model.Comment: 15pp., LaTeX, no figures, reference adde
Challenges of D=6 N=(1,1) SYM Theory
Maximally supersymmetric Yang-Mills theories have several remarkable
properties, among which are the cancellation of UV divergences, factorization
of higher loop corrections and possible integrability. Much attention has been
attracted to the N=4 D=4 SYM theory. The N=(1,1) D=6 SYM theory possesses
similar properties but is nonrenomalizable and serves as a toy model for
supergravity. We consider the on-shell four point scattering amplitude and
analyze its perturbative expansion within the spin-helicity and superspace
formalism. The integrands of the resulting diagrams coincide with those of the
N=4 D=4 SYM and obey the dual conformal invariance. Contrary to 4 dimensions,
no IR divergences on mass shell appear. We calculate analytically the leading
logarithmic asymptotics in all loops. Their summation leads to a Regge
trajectory which is calculated exactly. The leading powers of s are calculated
up to six loops. Their summation is performed numerically and leads to a smooth
function of s. The leading UV divergences are calculated up to 5 loops. The
result suggests the geometrical progression which ends up in a finite
expression. This leads us to a radical point of view on nonrenormalizable
theories.Comment: 11 pages, 2 figures, Late
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 operation.
Two-dimensional models and the four-dimensional 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 operation in a self-consistent way, as the
original recipe does the ultraviolet 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
Effective Action and Measure in Matrix Model of IIB Superstrings
We calculate an effective action and measure induced by the integration over
the auxiliary field in the matrix model recently proposed to describe IIB
superstrings. It is shown that the measure of integration over the auxiliary
matrix is uniquely determined by locality and reparametrization invariance of
the resulting effective action. The large-- limit of the induced measure for
string coordinates is discussed in detail. It is found to be ultralocal and,
thus, possibly is irrelevant in the continuum limit. The model of the GKM type
is considered in relation to the effective action problem.Comment: 9pp., Latex; v2: the discussion of the large N limit of the induced
measure is substantially expande
Quantum Fluctuations of a Coulomb Potential as a Source of Flicker Noise
The power spectrum of quantum fluctuations of the electromagnetic field
produced by an elementary particle is determined. It is found that in a wide
range of practically important frequencies the power spectrum of fluctuations
exhibits an inverse frequency dependence. The magnitude of fluctuations
produced by a conducting sample is shown to have a Gaussian distribution around
its mean value, and its dependence on the sample geometry is determined. In
particular, it is demonstrated that for geometrically similar samples the power
spectrum is inversely proportional to the sample volume. It is argued also that
the magnitude of fluctuations induced by external electric field is
proportional to the field strength squared. A comparison with experimental data
on flicker noise measurements in continuous metal films is made.Comment: 11 pages, substantially corrected and extende
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