244 research outputs found
Global algebras of nonlinear generalized functions with applications in general relativity
We give an overview of the development of algebras of generalized functions
in the sense of Colombeau and recent advances concerning diffeomorphism
invariant global algebras of generalized functions and tensor fields. We
furthermore provide a survey on possible applications in general relativity in
light of the limitations of distribution theory
Higher Poincare Lemma and Integrability
We prove the non-abelian Poincare lemma in higher gauge theory in two
different ways. The first method uses a result by Jacobowitz which states
solvability conditions for differential equations of a certain type. The second
method extends a proof by Voronov and yields the explicit gauge parameters
connecting a flat local connective structure to the trivial one. Finally, we
show how higher flatness appears as a necessary integrability condition of a
linear system which featured in recently developed twistor descriptions of
higher gauge theories.Comment: 1+21 pages, presentation streamlined, section on integrability for
higher linear systems significantly improved, published versio
On the completeness of impulsive gravitational wave space-times
We consider a class of impulsive gravitational wave space-times, which
generalize impulsive pp-waves. They are of the form ,
where is a Riemannian manifold of arbitrary dimension and carries
the line element with the line
element of and the Dirac measure. We prove a completeness result
for such space-times with complete Riemannian part .Comment: 13 pages, minor changes suggested by the referee
Adding flavour to twistor strings
Twistor string theory is known to describe a wide variety of field theories
at tree-level and has proved extremely useful in making substantial progress in
perturbative gauge theory. We explore the twistor dual description of a class
of N=2 UV-finite super-Yang-Mills theories with fundamental flavour by adding
'flavour' branes to the topological B-model on super-twistor space and comment
on the appearance of these objects. Evidence for the correspondence is provided
by matching amplitudes on both sides.Comment: 6 pages; contribution to the proceedings for the European Physical
Society conference on High Energy Physics in Manchester, 19-25 July 2007. v3:
Typos correcte
Validation of non-REM sleep stage decoding from resting state fMRI using linear support vector machines
A growing body of literature suggests that changes in consciousness are reflected in specific connectivity patterns of the brain as obtained from resting state fMRI (rs-fMRI). As simultaneous electroencephalography (EEG) is often unavailable, decoding of potentially confounding sleep patterns from rs-fMRI itself might be useful and improve data interpretation. Linear support vector machine classifiers were trained on combined rs-fMRI/EEG recordings from 25 subjects to separate wakefulness (S0) from non-rapid eye movement (NREM) sleep stages 1 (S1), 2 (S2), slow wave sleep (SW) and all three sleep stages combined (SX). Classifier performance was quantified by a leave-one-subject-out cross-validation (LOSO-CV) and on an independent validation dataset comprising 19 subjects. Results demonstrated excellent performance with areas under the receiver operating characteristics curve (AUCs) close to 1.0 for the discrimination of sleep from wakefulness (S0|SX), S0|S1, S0|S2 and S0|SW, and good to excellent performance for the classification between sleep stages (S1|S2:~0.9; S1|SW:~1.0; S2|SW:~0.8). Application windows of fMRI data from about 70 s were found as minimum to provide reliable classifications. Discrimination patterns pointed to subcortical-cortical connectivity and within-occipital lobe reorganization of connectivity as strongest carriers of discriminative information. In conclusion, we report that functional connectivity analysis allows valid classification of NREM sleep stages
Toric Calabi-Yau supermanifolds and mirror symmetry
We study mirror symmetry of supermanifolds constructed as fermionic
extensions of compact toric varieties. We mainly discuss the case where the
linear sigma A-model contains as many fermionic fields as there are U(1)
factors in the gauge group. In the mirror super-Landau-Ginzburg B-model, focus
is on the bosonic structure obtained after integrating out all the fermions.
Our key observation is that there is a relation between the super-Calabi-Yau
conditions of the A-model and quasi-homogeneity of the B-model, and that the
degree of the associated superpotential in the B-model is given in terms of the
determinant of the fermion charge matrix of the A-model.Comment: 20 pages, v2: references adde
Constructing Self-Dual Strings
We present an ADHMN-like construction which generates self-dual string
solutions to the effective M5-brane worldvolume theory from solutions to the
Basu-Harvey equation. Our construction finds a natural interpretation in terms
of gerbes, which we develop in some detail. We also comment on a possible
extension to stacks of multiple M5-branes.Comment: 1+19 pages, presentation improved, minor corrections, published
versio
Groupoids, Loop Spaces and Quantization of 2-Plectic Manifolds
We describe the quantization of 2-plectic manifolds as they arise in the
context of the quantum geometry of M-branes and non-geometric flux
compactifications of closed string theory. We review the groupoid approach to
quantizing Poisson manifolds in detail, and then extend it to the loop spaces
of 2-plectic manifolds, which are naturally symplectic manifolds. In
particular, we discuss the groupoid quantization of the loop spaces of R^3, T^3
and S^3, and derive some interesting implications which match physical
expectations from string theory and M-theory.Comment: 71 pages, v2: references adde
Fuzzy Torus via q-Parafermion
We note that the recently introduced fuzzy torus can be regarded as a
q-deformed parafermion. Based on this picture, classification of the Hermitian
representations of the fuzzy torus is carried out. The result involves
Fock-type representations and new finite dimensional representations for q
being a root of unity as well as already known finite dimensional ones.Comment: 12pages, no figur
A projective Dirac operator on CP^2 within fuzzy geometry
We propose an ansatz for the commutative canonical spin_c Dirac operator on
CP^2 in a global geometric approach using the right invariant (left action-)
induced vector fields from SU(3). This ansatz is suitable for noncommutative
generalisation within the framework of fuzzy geometry. Along the way we
identify the physical spinors and construct the canonical spin_c bundle in this
formulation. The chirality operator is also given in two equivalent forms.
Finally, using representation theory we obtain the eigenspinors and calculate
the full spectrum. We use an argument from the fuzzy complex projective space
CP^2_F based on the fuzzy analogue of the unprojected spin_c bundle to show
that our commutative projected spin_c bundle has the correct
SU(3)-representation content.Comment: reduced to 27 pages, minor corrections, minor improvements, typos
correcte
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