98 research outputs found
Supersymmetric QCD: Exact Results and Strong Coupling
We revisit two longstanding puzzles in supersymmetric gauge theories. The
first concerns the question of the holomorphy of the coupling, and related to
this the possible definition of an exact (NSVZ) beta function. The second
concerns instantons in pure gluodynamics, which appear to give sensible, exact
results for certain correlation functions, which nonetheless differ from those
obtained using systematic weak coupling expansions. For the first question, we
extend an earlier proposal of Arkani-Hamed and Murayama, showing that if their
regulated action is written suitably, the holomorphy of the couplings is
manifest, and it is easy to determine the renormalization scheme for which the
NSVZ formula holds. This scheme, however, is seen to be one of an infinite
class of schemes, each leading to an exact beta function; the NSVZ scheme,
while simple, is not selected by any compelling physical consideration. For the
second question, we explain why the instanton computation in the pure
supersymmetric gauge theory is not reliable, even at short distances. The
semiclassical expansion about the instanton is purely formal; if infrared
divergences appear, they spoil arguments based on holomorphy. We demonstrate
that infrared divergences do not occur in the perturbation expansion about the
instanton, but explain that there is no reason to think this captures all
contributions from the sector with unit topological charge. That one expects
additional contributions is illustrated by dilute gas corrections. These are
infrared divergent, and so difficult to define, but if non-zero give order one,
holomorphic, corrections to the leading result. Exploiting an earlier analysis
of Davies et al, we demonstrate that in the theory compactified on a circle of
radius beta, due to infrared effects, finite contributions indeed arise which
are not visible in the formal limit that beta goes to infinity.Comment: 28 pages, two references added, one typo correcte
Gross-Neveu Models, Nonlinear Dirac Equations, Surfaces and Strings
Recent studies of the thermodynamic phase diagrams of the Gross-Neveu model
(GN2), and its chiral cousin, the NJL2 model, have shown that there are phases
with inhomogeneous crystalline condensates. These (static) condensates can be
found analytically because the relevant Hartree-Fock and gap equations can be
reduced to the nonlinear Schr\"odinger equation, whose deformations are
governed by the mKdV and AKNS integrable hierarchies, respectively. Recently,
Thies et al have shown that time-dependent Hartree-Fock solutions describing
baryon scattering in the massless GN2 model satisfy the Sinh-Gordon equation,
and can be mapped directly to classical string solutions in AdS3. Here we
propose a geometric perspective for this result, based on the generalized
Weierstrass spinor representation for the embedding of 2d surfaces into 3d
spaces, which explains why these well-known integrable systems underlie these
various Gross-Neveu gap equations, and why there should be a connection to
classical string theory solutions. This geometric viewpoint may be useful for
higher dimensional models, where the relevant integrable hierarchies include
the Davey-Stewartson and Novikov-Veselov systems.Comment: 27 pages, 1 figur
Reliability of fluctuation-induced transport in a Maxwell-demon-type engine
We study the transport properties of an overdamped Brownian particle which is
simultaneously in contact with two thermal baths. The first bath is modeled by
an additive thermal noise at temperature . The second bath is associated
with a multiplicative thermal noise at temperature . The analytical
expressions for the particle velocity and diffusion constant are derived for
this system, and the reliability or coherence of transport is analyzed by means
of their ratio in terms of a dimensionless P\'{e}clet number. We find that the
transport is not very coherent, though one can get significantly higher
currents.Comment: 14 pages, 5 figure
What two models may teach us about duality violations in QCD
Though the operator product expansion is applicable in the calculation of
current correlation functions in the Euclidean region, when approaching the
Minkowskian domain, violations of quark-hadron duality are expected to occur,
due to the presence of bound-state or resonance poles. In QCD finite-energy sum
rules, contour integrals in the complex energy plane down to the Minkowskian
axis have to be performed, and thus the question arises what the impact of
duality violations may be. The structure and possible relevance of duality
violations is investigated on the basis of two models: the Coulomb system and a
model for light-quark correlators which has already been studied previously. As
might yet be naively expected, duality violations are in some sense "maximal"
for zero-width bound states and they become weaker for broader resonances whose
poles lie further away from the physical axis. Furthermore, to a certain
extent, they can be suppressed by choosing appropriate weight functions in the
finite-energy sum rules. A simplified Ansatz for including effects of duality
violations in phenomenological QCD sum rule analyses is discussed as well.Comment: 17 pages, 6 figures; version to appear in JHE
Cosmological parameters from the clustering of AGN
We attempt to put constraints on different cosmological and biasing models by
combining the recent clustering results of X-ray sources in the local () and distant universe ().Comment: 9 pages, 3 figures, to be published in the proceedings of the ''2nd
Hellenic Cosmology Workshop'', Athens 2001, eds, Manolis Plionis & Spiros
Kotsaki
Gravitational Waves from Gravitational Collapse
Gravitational wave emission from the gravitational collapse of massive stars
has been studied for more than three decades. Current state of the art
numerical investigations of collapse include those that use progenitors with
realistic angular momentum profiles, properly treat microphysics issues,
account for general relativity, and examine non--axisymmetric effects in three
dimensions. Such simulations predict that gravitational waves from various
phenomena associated with gravitational collapse could be detectable with
advanced ground--based and future space--based interferometric observatories.Comment: 68 pages including 13 figures; revised version accepted for
publication in Living Reviews in Relativity (http://www.livingreviews.org
Thermal properties and structure of cast carbon-containing invar and superinvar alloys after two-stage annealing
The NSVZ β-function and the Schwinger-Dyson equations for N = 1 SQED with N f flavors, regularized by higher derivatives
Varying constants, Gravitation and Cosmology
Fundamental constants are a cornerstone of our physical laws. Any constant
varying in space and/or time would reflect the existence of an almost massless
field that couples to matter. This will induce a violation of the universality
of free fall. It is thus of utmost importance for our understanding of gravity
and of the domain of validity of general relativity to test for their
constancy. We thus detail the relations between the constants, the tests of the
local position invariance and of the universality of free fall. We then review
the main experimental and observational constraints that have been obtained
from atomic clocks, the Oklo phenomenon, Solar system observations, meteorites
dating, quasar absorption spectra, stellar physics, pulsar timing, the cosmic
microwave background and big bang nucleosynthesis. At each step we describe the
basics of each system, its dependence with respect to the constants, the known
systematic effects and the most recent constraints that have been obtained. We
then describe the main theoretical frameworks in which the low-energy constants
may actually be varying and we focus on the unification mechanisms and the
relations between the variation of different constants. To finish, we discuss
the more speculative possibility of understanding their numerical values and
the apparent fine-tuning that they confront us with.Comment: 145 pages, 10 figures, Review for Living Reviews in Relativit
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