21 research outputs found
The period-index problem for twisted topological K-theory
We introduce and solve a period-index problem for the Brauer group of a
topological space. The period-index problem is to relate the order of a class
in the Brauer group to the degrees of Azumaya algebras representing it. For any
space of dimension d, we give upper bounds on the index depending only on d and
the order of the class. By the Oka principle, this also solves the period-index
problem for the analytic Brauer group of any Stein space that has the homotopy
type of a finite CW-complex. Our methods use twisted topological K-theory,
which was first introduced by Donovan and Karoubi. We also study the cohomology
of the projective unitary groups to give cohomological obstructions to a class
being represented by an Azumaya algebra of degree n. Applying this to the
finite skeleta of the Eilenberg-MacLane space K(Z/l,2), where l is a prime, we
construct a sequence of spaces with an order l class in Br, but whose indices
tend to infinity.Comment: To appear in Geometry & Topology; minor cosmetic change
Cohomological obstruction theory for Brauer classes and the period-index problem
Let U be a connected scheme of finite cohomological dimension in which every
finite set of points is contained in an affine open subscheme. Suppose that
alpha is a class in H^2(U_et,Gm)_{tors}. For each positive integer m, the
K-theory of alpha-twisted sheaves is used to identify obstructions to alpha
being representable by an Azumaya algebra of rank m^2. The etale index of
alpha, denoted eti(alpha), is the least positive integer such that all the
obstructions vanish. Let per(alpha) be the order of alpha in
H^2(U_{et},Gm)_{tors}. Methods from stable homotopy theory give an upper bound
on the etale index that depends on the period of alpha and the etale
cohomological dimension of U; this bound is expressed in terms of the exponents
of the stable homotopy groups of spheres and the exponents of the stable
homotopy groups of B(Z/per(alpha)). As a corollary, if U is the spectrum of a
field of finite cohomological dimension d, then eti(alpha) divides
per(alpha)^[d/2], where [d/2] is the integer part of d/2, whenever per(alpha)
is divided neither by the characteristic of k nor by any primes that are small
relative to d.Comment: 15 pages. To appear in J. K-Theor
Low-Energy Supersymmetry Breaking from String Flux Compactifications: Benchmark Scenarios
Soft supersymmetry breaking terms were recently derived for type IIB string
flux compactifications with all moduli stabilised. Depending on the choice of
the discrete input parameters of the compactification such as fluxes and ranks
of hidden gauge groups, the string scale was found to have any value between
the TeV and GUT scales. We study the phenomenological implications of these
compactifications at low energy. Three realistic scenarios can be identified
depending on whether the Standard Model lies on D3 or D7 branes and on the
value of the string scale. For the MSSM on D7 branes and the string scale
between 10^12 GeV and 10^17 GeV we find that the LSP is a neutralino, while for
lower scales it is the stop. At the GUT scale the results of the fluxed MSSM
are reproduced, but now with all moduli stabilised. For the MSSM on D3 branes
we identify two realistic scenarios. The first one corresponds to an
intermediate string scale version of split supersymmetry. The second is a
stringy mSUGRA scenario. This requires tuning of the flux parameters to obtain
the GUT scale. Phenomenological constraints from dark matter, (g-2)_mu and
BR(b->s gamma) are considered for the three scenarios. We provide benchmark
points with the MSSM spectrum, making the models suitable for a detailed
phenomenological analysis.Comment: 29 pages, 12 figures, reference adde
Sparticle Spectra and LHC Signatures for Large Volume String Compactifications
We study the supersymmetric particle spectra and LHC collider observables for
the large-volume string models with a fundamental scale of 10^{11} GeV that
arise in moduli-fixed string compactifications with branes and fluxes. The
presence of magnetic fluxes on the brane world volume, required for chirality,
perturb the soft terms away from those previously computed in the dilute-flux
limit. We use the difference in high-scale gauge couplings to estimate the
magnitude of this perturbation and study the potential effects of the magnetic
fluxes by generating many random spectra with the soft terms perturbed around
the dilute flux limit. Even with a 40% variation in the high-scale soft terms
the low-energy spectra take a clear and predictive form. The resulting spectra
are broadly similar to those arising on the SPS1a slope, but more degenerate.
In their minimal version the models predict the ratios of gaugino masses to be
M_1 : M_2 : M_3=(1.5 - 2) : 2 : 6, different to both mSUGRA and mirage
mediation. Among the scalars, the squarks tend to be lighter and the sleptons
heavier than for comparable mSUGRA models. We generate 10 fb^{-1} of sample LHC
data for the random spectra in order to study the range of collider
phenomenology that can occur. We perform a detailed mass reconstruction on one
example large-volume string model spectrum. 100 fb^{-1} of integrated
luminosity is sufficient to discriminate the model from mSUGRA and aspects of
the sparticle spectrum can be accurately reconstructed.Comment: 42 pages, 21 figures. Added references and discussion for section 3.
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Patterns of expression of cell cycle/apoptosis genes along the spectrum of thyroid carcinoma progression
Genetic screening studies suggest that genetic changes underlie progression from well differentiated to anaplastic thyroid cancers. The aim of this study is to determine to what extent cell cycle/apoptosis regulators contribute to cancer progression. Tissue microarrarys (TMAs) were constructed from well-differentiated papillary thyroid carcinoma (WDPTC; n = 41), poorly differentiated thyroid carcinoma (PDTC; n = 43), and anaplastic thyroid carcinoma (ATC; n = 22). TMAs were immunostained for 7 different cell cycle/apoptosis-related genes (p53, Ki-67, bcl-2, mdm-2, cyclin D1, p21, and p27). p53 (0%, 12%, 32%) and Ki-67 (5%, 49%, 82%) were expressed with increasing frequency, and bcl-2 (68%, 42%, 0%) and p21 (40%, 7%, 0%) with decreasing frequency in WDPTC to PDTC and ATC, respectively (P < .001). Interestingly, mdm-2 (54%, 5%, 0%) showed decreased expression along the progression axis (P < .001). p27 and cyclin D1 were expressed in <15% of cases, with a trend toward decreasing expression from WDPTC to PDTC to ATC. These data confirm the presence of increasing genetic complexity with progressive dedifferentiation in thyroid cancer, with aberrant tumor suppressor activity and increased proliferative activity being most prevalent in ATC. The data also confirm the intermediate position of PDTC in the classification scheme of thyroid carcinoma