11,753 research outputs found
Free Fermions and Extended Conformal Algebras
A class of algebras is constructed using free fermions and the invariant
antisymmetric tensors associated with irreducible holonomy groups. (This
version contains minor typographical corrections and some additional
references. )Comment: 7 pages, KCL-Th-94-1
Twistor spaces for HKT manifolds
We construct the twistor space associated with an HKT manifold, that is, a
hyper-K\"ahler manifold with torsion, a type of geometry that arises as the
target space geometry in two-dimensional sigma models with (4,0) supersymmetry.
We show that this twistor space has a natural complex structure and is a
holomorphic fibre bundle over the complex projective line with fibre the
associated HKT manifold. We also show how the metric and torsion of the HKT
manifold can be determined from data on the twistor space by a reconstruction
theorem. We give a geometric description of the sigma model (4,0) superfields
as holomorphic maps (suitably understood) from a twistorial extension of (4,0)
superspace (harmonic superspace) into the twistor space of the sigma model
target manifold and write an action for the sigma model in terms of these (4,0)
superfields.Comment: 15 pages, Phyzz
(N,p,q) Harmonic Superspace
A family of harmonic superspaces associated with four-dimensional spacetime
is described. Some applications to supersymmetric field theories, including
supergravity, are given.Comment: 25 pages, latex file, improved. Minor text errors correcte
A note on the UV behaviour of maximally supersymmetric Yang-Mills theories
The question of whether BPS invariants are protected in maximally
supersymmetric Yang-Mills theories is investigated from the point of view of
algebraic renormalisation theory. The protected invariants are those whose
cohomology type differs from that of the action. It is confirmed that one-half
BPS invariants () are indeed protected while the double-trace one-quarter
BPS invariant () is not protected at two loops in D=7, but is protected
at three loops in D=6 in agreement with recent calculations. Non-BPS
invariants, i.e. full superspace integrals, are also shown to be unprotected.Comment: 12 pages. Minor changes to text. References adde
Patching DFT, T-duality and Gerbes
We clarify the role of the dual coordinates as described from the
perspectives of the Buscher T-duality rules and Double Field Theory. We show
that the T-duality angular dual coordinates cannot be identified with Double
Field Theory dual coordinates in any of the proposals that have been made in
the literature for patching the doubled spaces. In particular, we show with
explicit examples that the T-duality angular dual coordinates can have
non-trivial transition functions over a spacetime and that their identification
with the Double Field Theory dual coordinates is in conflict with proposals in
which the latter remain inert under the patching of the B-field. We then
demonstrate that the Double Field Theory coordinates can be identified with
some C-space coordinates and that the T-dual spaces of a spacetime are
subspaces of the gerbe in C-space. The construction provides a description of
both the local symmetry and the T-dual spaces of spacetime.Comment: minor changes, references adde
Basic JCL for the CRAY-1 operating system (COS) with emphasis on making the transition from CDC 7600/SCOPE
Users of the CDC 7600 at Ames are assisted in making the transition to the CRAY-1. Similarities and differences in the basic JCL are summarized, and a dozen or so examples of typical batch jobs for the two systems are shown in parallel. Some changes to look for in FORTRAN programs and in the use of UPDATE are also indicated. No attempt is made to cover magnetic tape handling. The material here should not be considered a substitute for reading the more conventional manuals or the User's Guide for the Advanced Computational Facility, available from the Computer Information Center
Twistor Spaces for QKT Manifolds
We find that the target space of two-dimensional (4,0) supersymmetric sigma
models with torsion coupled to (4,0) supergravity is a QKT manifold, that is, a
quaternionic K\"ahler manifold with torsion. We give four examples of
geodesically complete QKT manifolds one of which is a generalisation of the
LeBrun geometry. We then construct the twistor space associated with a QKT
manifold and show that under certain conditions it is a K\"ahler manifold with
a complex contact structure. We also show that, for every 4k-dimensional QKT
manifold, there is an associated 4(k+1)-dimensional hyper-K\"ahler one.Comment: 25 pages, phyzz
Manifold Learning in MR spectroscopy using nonlinear dimensionality reduction and unsupervised clustering
Purpose To investigate whether nonlinear dimensionality reduction improves unsupervised classification of 1H MRS brain tumor data compared with a linear method. Methods In vivo single-voxel 1H magnetic resonance spectroscopy (55 patients) and 1H magnetic resonance spectroscopy imaging (MRSI) (29 patients) data were acquired from histopathologically diagnosed gliomas. Data reduction using Laplacian eigenmaps (LE) or independent component analysis (ICA) was followed by k-means clustering or agglomerative hierarchical clustering (AHC) for unsupervised learning to assess tumor grade and for tissue type segmentation of MRSI data. Results An accuracy of 93% in classification of glioma grade II and grade IV, with 100% accuracy in distinguishing tumor and normal spectra, was obtained by LE with unsupervised clustering, but not with the combination of k-means and ICA. With 1H MRSI data, LE provided a more linear distribution of data for cluster analysis and better cluster stability than ICA. LE combined with k-means or AHC provided 91% accuracy for classifying tumor grade and 100% accuracy for identifying normal tissue voxels. Color-coded visualization of normal brain, tumor core, and infiltration regions was achieved with LE combined with AHC. Conclusion Purpose To investigate whether nonlinear dimensionality reduction improves unsupervised classification of 1H MRS brain tumor data compared with a linear method. Methods In vivo single-voxel 1H magnetic resonance spectroscopy (55 patients) and 1H magnetic resonance spectroscopy imaging (MRSI) (29 patients) data were acquired from histopathologically diagnosed gliomas. Data reduction using Laplacian eigenmaps (LE) or independent component analysis (ICA) was followed by k-means clustering or agglomerative hierarchical clustering (AHC) for unsupervised learning to assess tumor grade and for tissue type segmentation of MRSI data. Results An accuracy of 93% in classification of glioma grade II and grade IV, with 100% accuracy in distinguishing tumor and normal spectra, was obtained by LE with unsupervised clustering, but not with the combination of k-means and ICA. With 1H MRSI data, LE provided a more linear distribution of data for cluster analysis and better cluster stability than ICA. LE combined with k-means or AHC provided 91% accuracy for classifying tumor grade and 100% accuracy for identifying normal tissue voxels. Color-coded visualization of normal brain, tumor core, and infiltration regions was achieved with LE combined with AHC. Conclusion The LE method is promising for unsupervised clustering to separate brain and tumor tissue with automated color-coding for visualization of 1H MRSI data after cluster analysis
ELLIPTIC MONOPOLES AND (4,0)-SUPERSYMMETRIC SIGMA MODELS WITH TORSION
We explicitly construct the metric and torsion couplings of two-dimensional
(4,0)-super\-sym\-metric sigma models with target space a four-manifold that
are invariant under a symmetry generated by a tri-holomorphic Killing
vector field that leaves in addition the torsion invariant. We show that the
metric couplings arise from magnetic monopoles on the three-sphere which is the
space of orbits of the group action generated by the tri-holomorphic Killing
vector field on the sigma model target manifold. We also examine the global
structure of a subclass of these metrics that are in addition -invariant
and find that the only non-singular one, for models with non-zero torsion, is
that of WZW model.Comment: 12 pages, phyzz
Anomalies and divergences in N=4 supergravity
The invariants in D=4, N=4 supergravity are discussed up to the three-loop
order (where one expects a general R^4 structure). Because there is an anomaly
in the rigid SL(2,R) symmetry of this theory, the analysis of possible
restrictions on three-loop divergences due to duality needs careful treatment.
We show that this anomalous symmetry is still strong enough at the three-loop
order to require duality invariance of candidate counterterms. Provided one
makes the additional assumption that there exists a full 16-supercharge
off-shell formulation of the theory, counterterms at L \ge 2 loops would also
have to be writable as full-superspace integrals. At the three-loop order such
a duality-invariant full-superspace integral candidate counterterm exists, but
its duality invariance is marginal in the sense that the full-superspace
counter-Lagrangian is not itself duality invariant. We show that, subject to
the assumption that a full off-shell quantisation formalism exists, such
marginal invariants are not allowable as counterterms.Comment: 15 pages, version published in Phys. Lett.
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