4,762 research outputs found
Energies of knot diagrams
We introduce and begin the study of new knot energies defined on knot
diagrams. Physically, they model the internal energy of thin metallic solid
tori squeezed between two parallel planes. Thus the knots considered can
perform the second and third Reidemeister moves, but not the first one. The
energy functionals considered are the sum of two terms, the uniformization term
(which tends to make the curvature of the knot uniform) and the resistance term
(which, in particular, forbids crossing changes). We define an infinite family
of uniformization functionals, depending on an arbitrary smooth function
and study the simplest nontrivial case , obtaining neat normal forms
(corresponding to minima of the functional) by making use of the Gauss
representation of immersed curves, of the phase space of the pendulum, and of
elliptic functions
Comparative Planetary Atmospheres: Models of TrES-1 and HD209458b
We present new self-consistent atmosphere models for transiting planets
TrES-1 and HD209458b. The planets were recently observed with the Spitzer Space
Telescope in bands centered on 4.5 and 8.0 m, for TrES-1, and 24 m,
for HD209458b. We find that standard solar metallicity models fit the
observations for HD209458b. For TrES-1, which has an T_eff ~300 K cooler, we
find that models with a metallicity 3-5 times enhanced over solar abundances
can match the 1 error bar at 4.5 m and 2 at 8.0m.
Models with solar abundances that included energy deposition into the
stratosphere give fluxes that fall within the 2 error bars in both
bands. The best-fit models for both planets assume that reradiation of absorbed
stellar flux occurs over the entire planet. For all models of both planets we
predict planet/star flux ratios in other Spitzer bandpasses.Comment: Accepted to the Astrophysical Journal Letters, May 17, 200
Nonrelativistic Limit of the Scalar Chern-Simons Theory and the Aharonov-Bohm Scattering
We study the nonrelativistic limit of the quantum theory of a Chern-Simons
field minimally coupled to a scalar field with quartic self-interaction. The
renormalization of the relativistic model, in the Coulomb gauge, is discussed.
We employ a procedure to calculate scattering amplitudes for low momenta that
generates their expansion and separates the contributions coming from
high and low energy intermediary states. The two body scattering amplitude is
calculated up to order . It is shown that the existence of a critical
value of the self-interaction parameter for which the 2-particle scattering
amplitude reduces to the Aharonov-Bohm one is a strictly nonrelativistic
feature. The subdominant terms correspond to relativistic corrections to the
Aharonov-Bohm scattering. A nonrelativistic reduction scheme and an effective
nonrelativistic Lagrangian to account for the relativistic corrections are
proposed.Comment: 22 pages, 8 figures, revtex, to be published in Int. J. Mod. Phys.
Holography and Defect Conformal Field Theories
We develop both the gravity and field theory sides of the Karch-Randall
conjecture that the near-horizon description of a certain D5-D3 brane
configuration in string theory, realized as AdS_5 x S^5 bisected by an AdS_4 x
S^2 "brane", is dual to N=4 Super Yang-Mills theory in R^4 coupled to an R^3
defect. We propose a complete Lagrangian for the field theory dual, a novel
"defect superconformal field theory" wherein a subset of the fields of N=4 SYM
interacts with a d=3 SU(N) fundamental hypermultiplet on the defect preserving
conformal invariance and 8 supercharges. The Kaluza-Klein reduction of wrapped
D5 modes on AdS_4 x S^2 leads to towers of short representations of OSp(4|4),
and we construct the map to a set of dual gauge-invariant defect operators O_3
possessing integer conformal dimensions. Gravity calculations of and
are given. Spacetime and N-dependence matches expectations from dCFT,
while the behavior as functions of lambda = g^2 N at strong and weak coupling
is generically different. We comment on a class of correlators for which a
non-renormalization theorem may still exist. Partial evidence for the
conformality of the quantum theory is given, including a complete argument for
the special case of a U(1) gauge group. Some weak coupling arguments which
illuminate the duality are presented.Comment: 47 pages, LaTeX, 2 figures, feynmf. v2: fixed minor errors, added
references. v3: fixed more typo
Atmosphere, Interior, and Evolution of the Metal-Rich Transiting Planet HD 149026b
We investigate the atmosphere and interior of the new transiting planet HD
149026b, which appears to be very rich in heavy elements. We first compute
model atmospheres at metallicities ranging from solar to ten times solar, and
show how for cases with high metallicity or inefficient redistribution of
energy from the day side, the planet may develop a hot stratosphere due to
absorption of stellar flux by TiO and VO. The spectra predicted by these models
are very different than cooler atmosphere models without stratospheres. The
spectral effects are potentially detectable with the Spitzer Space Telescope.
In addition the models with hot stratospheres lead to a large limb brightening,
rather than darkening. We compare the atmosphere of HD 149026b to other
well-known transiting planets, including the recently discovered HD 189733b,
which we show have planet-to-star flux ratios twice that of HD 209458 and
TrES-1. The methane abundance in the atmosphere of HD 189733b is a sensitive
indicator of atmospheric temperature and metallicity and can be constrained
with Spitzer IRAC observations. We then turn to interior studies of HD 149026b
and use a grid of self-consistent model atmospheres and high-pressure equations
of state for all components to compute thermal evolution models of the planet.
We estimate that the mass of heavy elements within the planet is in the range
of 60 to 93 M_earth. Finally, we discuss trends in the radii of transiting
planets with metallicity in light of this new member of the class.Comment: Accepted to the Astrophysical Journal. 18 pages, including 10
figures. New section on the atmosphere of planet HD 189733b. Enhanced
discussion of atmospheric Ti chemistry and core mass for HD 149026
CFT/CFT interpolating RG flows and the holographic c-function
We consider holographic RG flows which interpolate between non-trivial
ultra-violet (UV) and infra-red (IR) conformal fixed points. We study the
``superpotentials'' which characterize different flows and discuss their
expansions near the fixed points. Then we focus on the holographic -function
as defined from the two-point function of the stress-energy tensor. We point
out that the equation for the metric fluctuations in the background flow is
equivalent to a scattering problem and we use this to obtain an expression for
the -function in terms of the associated Jost functions. We propose two
explicit models that realize UV-IR flows. In the first example we consider a
thin wall separating two AdS spaces with different radii, while in the second
one the UV region is replaced with an asymptotically AdS space. We find that
the holographic -function obeys the expected properties. In particular it
reduces to the correct -- nonzero -- central charge in the IR limit.Comment: 20 pages, discussion at the end of sec. 3 and sec. 4.1 change
The Equation of State for Dense QCD and Quark Stars
We calculate the equation of state for degenerate quark matter to leading
order in hard-dense-loop (HDL) perturbation theory. We solve the
Tolman-Oppenheimer-Volkov equations to obtain the mass-radius relation for
dense quark stars. Both the perturbative QCD and the HDL equations of state
have a large variation with respect to the renormalization scale for quark
chemical potential below 1 GeV which leads to large theoretical uncertainties
in the quark star mass-radius relation.Comment: 7 pages, 3 figure
Space-time dependent couplings in N=1 SUSY gauge theories: Anomalies and Central Functions
We consider N=1 supersymmetric gauge theories in which the couplings are
allowed to be space-time dependent functions. Both the gauge and the
superpotential couplings become chiral superfields. As has recently been shown,
a new topological anomaly appears in models with space-time dependent gauge
coupling. Here we show how this anomaly may be used to derive the NSVZ beta
function in a particular, well-determined renormalisation scheme, both without
and with chiral matter. Moreover we extend the topological anomaly analysis to
theories coupled to a classical curved superspace background, and use it to
derive an all-order expression for the central charge c, the coefficient of the
Weyl tensor squared contribution to the conformal anomaly. We also comment on
the implications of our results for the central charge a expected to be of
relevance for a four-dimensional C-theorem.Comment: 28 pages, LaTeX, no figure
Weak Lensing, Shear and the Cosmic Virial Theorem in a Model with a Scale-Dependent Gravitational Coupling
It is argued that, in models where the gravitational coupling is
scale-dependent, predictions concerning weak gravitational lensing and shear
are essentially similar to the ones derived from General Relativity. This is
consistent with recent negative results of observations of the MS1224, CL2218
and A1689 systems aimimg to infer from those methods the presence of dark
matter. It is shown, however, that the situation is quite different when an
analysis based on the Cosmic Virial Theorem is concerned.Comment: Footnote and references added. Version to in Gen. Relativity and
Gravitation Vol. 29 (1997
Star product and the general Leigh-Strassler deformation
We extend the definition of the star product introduced by Lunin and
Maldacena to study marginal deformations of N=4 SYM. The essential difference
from the latter is that instead of considering U(1)xU(1) non-R-symmetry, with
charges in a corresponding diagonal matrix, we consider two Z_3-symmetries
followed by an SU(3) transformation, with resulting off-diagonal elements. From
this procedure we obtain a more general Leigh-Strassler deformation, including
cubic terms with the same index, for specific values of the coupling constants.
We argue that the conformal property of N=4 SYM is preserved, in both beta-
(one-parameter) and gamma_{i}-deformed (three-parameters) theories, since the
deformation for each amplitude can be extracted in a prefactor. We also
conclude that the obtained amplitudes should follow the iterative structure of
MHV amplitudes found by Bern, Dixon and Smirnov.Comment: 21 pages, no figures, JHEP3, v2: references added, v3: appendix A
added, v4: clarification in section 3.
- âŠ