422 research outputs found
Cycles in the chamber homology of GL(3)
Let F be a nonarchimedean local field and let GL(N) = GL(N,F). We prove the
existence of parahoric types for GL(N). We construct representative cycles in
all the homology classes of the chamber homology of GL(3).Comment: 45 pages. v3: minor correction
Asymptotics and local constancy of characters of p-adic groups
In this paper we study quantitative aspects of trace characters
of reductive -adic groups when the representation varies. Our approach
is based on the local constancy of characters and we survey some other related
results. We formulate a conjecture on the behavior of relative to
the formal degree of , which we are able to prove in the case where
is a tame supercuspidal. The proof builds on J.-K.~Yu's construction and the
structure of Moy-Prasad subgroups.Comment: Proceedings of Simons symposium on the trace formul
The supercuspidal representations of p-adic classical groups
Let G be a unitary, symplectic or special orthogonal group over a locally
compact non-archimedean local field of odd residual characteristic. We
construct many new supercuspidal representations of G, and Bushnell-Kutzko
types for these representations. Moreover, we prove that every irreducible
supercuspidal representation of G arises from our constructions.Comment: 55 pages -- minor changes from 1st version (mostly in sections 2.2,
4.2 and 6.2). To appear in Inventiones mathematicae, 2008 (DOI is not yet
active as at 12 Nov 2007
Spectral curves and the mass of hyperbolic monopoles
The moduli spaces of hyperbolic monopoles are naturally fibred by the
monopole mass, and this leads to a nontrivial mass dependence of the
holomorphic data (spectral curves, rational maps, holomorphic spheres)
associated to hyperbolic multi-monopoles. In this paper, we obtain an explicit
description of this dependence for general hyperbolic monopoles of magnetic
charge two. In addition, we show how to compute the monopole mass of higher
charge spectral curves with tetrahedral and octahedral symmetries. Spectral
curves of euclidean monopoles are recovered from our results via an
infinite-mass limit.Comment: 43 pages, LaTeX, 3 figure
Transfer-Matrix Monte Carlo Estimates of Critical Points in the Simple Cubic Ising, Planar and Heisenberg Models
The principle and the efficiency of the Monte Carlo transfer-matrix algorithm
are discussed. Enhancements of this algorithm are illustrated by applications
to several phase transitions in lattice spin models. We demonstrate how the
statistical noise can be reduced considerably by a similarity transformation of
the transfer matrix using a variational estimate of its leading eigenvector, in
analogy with a common practice in various quantum Monte Carlo techniques. Here
we take the two-dimensional coupled -Ising model as an example.
Furthermore, we calculate interface free energies of finite three-dimensional
O() models, for the three cases , 2 and 3. Application of finite-size
scaling to the numerical results yields estimates of the critical points of
these three models. The statistical precision of the estimates is satisfactory
for the modest amount of computer time spent
Non-linear bigravity and cosmic acceleration
We explore the cosmological solutions of classes of non-linear bigravity
theories. These theories are defined by effective four-dimensional Lagrangians
describing the coupled dynamics of two metric tensors, and containing, in the
linearized limit, both a massless graviton and an ultralight one. We focus on
two paradigmatic cases: the case where the coupling between the two metrics is
given by a Pauli-Fierz-type mass potential, and the case where this coupling
derives from five-dimensional brane constructions. We find that cosmological
evolutions in bigravity theories can be described in terms of the dynamics of
two ``relativistic particles'', moving in a curved Lorenzian space, and
connected by some type of nonlinear ``spring''. Classes of bigravity
cosmological evolutions exhibit a ``locking'' mechanism under which the two
metrics ultimately stabilize in a bi-de-Sitter configuration, with relative
(constant) expansion rates. In the absence of matter, we find that a generic
feature of bigravity cosmologies is to exhibit a period of cosmic acceleration.
This leads us to propose bigravity as a source of a new type of dark energy
(``tensor quintessence''), exhibiting specific anisotropic features. Bigravity
could also have been the source of primordial inflation.Comment: 55 pages, 4 figures, references and comments added, final version
published in Phys. Rev.
How does the early life environment influence the oral microbiome and determine oral health outcomes in childhood?
The first 1000 days of life, from conception to 2 years, are a critical window for the influence of environmental exposures on the assembly of the oral microbiome, which is the precursor to dental caries (decay), one of the most prevalentmicrobially induced disorders worldwide. While it is known that the human microbiome is susceptible to environmental exposures, there is limited understanding of the impact of prenatal and early childhood exposures on the oral microbiome trajectory and oral health. A barrier has been the lack of technology to directly measure the foetal "exposome", which includes nutritional and toxic exposures crossing the placenta. Another barrier has been the lack of statistical methods to account for the high dimensional data generated by-omic assays. Through identifying which early life exposures influence the oral microbiome and modify oral health, these findings can be translated into interventions to reduce dental decay prevalence.Christina Jane Adler, Kim-Anh Lê Cao, Toby Hughes, Piyush Kumar, Christine Austi
Symmetry restoration of the soft pion corrections for the light sea quark distributions in the small region
The soft pion correction at high energy may play a crucial role in
non-perturbative parts of sea quark distributions. In this paper, we show that,
while the soft pion correction for the strange sea qaurk distribution is
suppressed in the large and the medium region compared with that for the up
and the down sea quark one, it can become large and SU(3) flavor symmetric in
the very small region. This gives us a good reason for the symmetry
restoration of light sea quark distributions required by the mean charge sum
rule for the light sea quarks. Then, by estimating this sum rule with the help
of the results obtained by the soft pion correction, it is argued that there is
a large symmetry restoration of the strange sea quark in the region from
to at GeV.Comment: 22 pages including 4 eps figures, ReVTeX, to appear in Phys. Rev.
Spectral quark model and low-energy hadron phenomenology
We propose a spectral quark model which can be applied to low energy hadronic
physics. The approach is based on a generalization of the Lehmann
representation of the quark propagator. We work at the one-quark-loop level.
Electromagnetic and chiral invariance are ensured with help of the gauge
technique which provides particular solutions to the Ward-Takahashi identities.
General conditions on the quark spectral function follow from natural physical
requirements. In particular, the function is normalized, its all positive
moments must vanish, while the physical observables depend on negative moments
and the so-called log-moments. As a consequence, the model is made finite,
dispersion relations hold, chiral anomalies are preserved, and the twist
expansion is free from logarithmic scaling violations, as requested of a
low-energy model. We study a variety of processes and show that the framework
is very simple and practical. Finally, incorporating the idea of vector-meson
dominance, we present an explicit construction of the quark spectral function
which satisfies all the requirements. The corresponding momentum representation
of the resulting quark propagator exhibits only cuts on the physical axis, with
no poles present anywhere in the complex momentum space. The momentum-dependent
quark mass compares very well to recent lattice calculations. A large number of
predictions and relations can be deduced from our approach for such quantities
as the pion light-cone wave function, non-local quark condensate, pion
transition form factor, pion valence parton distribution function, etc.Comment: revtex, 24 pages, 3 figure
The Determination of alpha_s from Tau Decays Revisited
We revisit the determination of alpha_s(m_tau) using a fit to inclusive tau
hadronic spectral moments in light of (1) the recent calculation of the
fourth-order perturbative coefficient K_4 in the expansion of the Adler
function, (2) new precision measurements from BABAR of e+e- annihilation cross
sections, which decrease the uncertainty in the separation of vector and
axial-vector spectral functions, and (3) improved results from BABAR and Belle
on tau branching fractions involving kaons. We estimate that the fourth-order
perturbative prediction reduces the theoretical uncertainty, introduced by the
truncation of the series, by 20% with respect to earlier determinations. We
discuss to some detail the perturbative prediction and show that the effect of
the incomplete knowledge of the series is reduced by using the so-called
contour-improved calculation, as opposed to fixed-order perturbation theory
which manifests convergence problems. The corresponding theoretical
uncertainties are studied at the tau and Z mass scales. Nonperturbative
contributions extracted from the most inclusive fit are small, in agreement
with earlier determinations. Systematic effects from quark-hadron duality
violation are estimated with simple models and found to be within the quoted
systematic errors. The fit gives alpha_s(m_tau) = 0.344 +- 0.005 +- 0.007,
where the first error is experimental and the second theoretical. After
evolution to M_Z we obtain alpha_s(M_Z) = 0.1212 +- 0.0005 +- 0.0008 +- 0.0005,
where the errors are respectively experimental, theoretical and due to the
evolution. The result is in agreement with the corresponding NNNLO value
derived from essentially the Z width in the global electroweak fit. The
alpha_s(M_Z) determination from tau decays is the most precise one to date.Comment: 22 pages, 7 figure
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