18,211 research outputs found
U-Duality and Integral Structures
We analyze the U-duality group for the case of a type II superstring
compactified to four dimensions on a K3 surface times a torus. The various
limits of this theory are considered which have interpretations as type IIA and
IIB superstrings, the heterotic string, and eleven-dimensional supergravity,
allowing all these theories to be directly related to each other. The integral
structure which appears in the Ramond-Ramond sector of the type II superstring
is related to the quantum cohomology of general Calabi-Yau threefolds which
allows the moduli space of type II superstring compactifications on Calabi-Yau
manifolds to be analyzed.Comment: 14 pages, latex once only (Revision has minor changes and an added
reference
The SQE and Creativity: A Race to the Bottom?
This paper explores the use of assessment methods in law modules which explicitly value and encourage creativity and innovation. It does so in the context of the Solicitors Qualifying Examination (SQE) and argues that the type of learning and teaching likely to be promoted by this âSuper Examâ is the exact opposite of the deep learning and critical thinking that higher education should foster. The paper draws on some of the recommendations of the Legal Education and Training Review (LETR) and a service review evaluating the introduction of poster presentations as a replacement for a multiple-choice question (MCQ) test as an assessment method into the Medical Law module at Leeds Beckett University and highlights the value of encouraging creativity in order to foster a wide variety of valuable skills
Mirror Symmetry and the Type II String
If and are a mirror pair of Calabi--Yau threefolds, mirror symmetry
should extend to an isomorphism between the type IIA string theory compactified
on and the type IIB string theory compactified on , with all
nonperturbative effects included. We study the implications which this proposal
has for the structure of the semiclassical moduli spaces of the compactified
type II theories. For the type IIB theory, the form taken by discrete shifts in
the Ramond-Ramond scalars exhibits an unexpected dependence on the -field.
(Based on a talk at the Trieste Workshop on S-Duality and Mirror Symmetry.)Comment: 8 pages, LaTeX using espcrc2.st
Vacuum field energy and spontaneous emission in anomalously dispersive cavities
Anomalously dispersive cavities, particularly white light cavities, may have
larger bandwidth to finesse ratios than their normally dispersive counterparts.
Partly for this reason, their use has been proposed for use in LIGO-like
gravity wave detectors and in ring-laser gyroscopes. In this paper we analyze
the quantum noise associated with anomalously dispersive cavity modes. The
vacuum field energy associated with a particular cavity mode is proportional to
the cavity-averaged group velocity of that mode. For anomalously dispersive
cavities with group index values between 1 and 0, this means that the total
vacuum field energy associated with a particular cavity mode must exceed . For white light cavities in particular, the group index approaches
zero and the vacuum field energy of a particular spatial mode may be
significantly enhanced. We predict enhanced spontaneous emission rates into
anomalously dispersive cavity modes and broadened laser linewidths when the
linewidth of intracavity emitters is broader than the cavity linewidth.Comment: 9 pages, 4 figure
Five-Dimensional Supersymmetric Gauge Theories and Degenerations of Calabi-Yau Spaces
We discuss five-dimensional supersymmetric gauge theories. An anomaly renders
some theories inconsistent and others consistent only upon including a
Wess-Zumino type Chern-Simons term. We discuss some necessary conditions for
existence of nontrivial renormalization group fixed points and find all
possible gauge groups and matter content which satisfy them. In some cases, the
existence of these fixed points can be inferred from string duality
considerations. In other cases, they arise from M-theory on Calabi-Yau
threefolds. We explore connections between aspects of the gauge theory and
Calabi-Yau geometry. A consequence of our classification of field theories with
nontrivial fixed points is a fairly complete classification of a class of
singularities of Calabi-Yau threefolds which generalize the ``del Pezzo
contractions'' and occur at higher codimension walls of the K\"{a}hler cone.Comment: harvmac, 52 pp., 5 figures (reference added
Breakup of Shearless Meanders and "Outer" Tori in the Standard Nontwist Map
The breakup of shearless invariant tori with winding number
(in continued fraction representation) of the
standard nontwist map is studied numerically using Greene's residue criterion.
Tori of this winding number can assume the shape of meanders (folded-over
invariant tori which are not graphs over the x-axis in phase space),
whose breakup is the first point of focus here. Secondly, multiple shearless
orbits of this winding number can exist, leading to a new type of breakup
scenario. Results are discussed within the framework of the renormalization
group for area-preserving maps. Regularity of the critical tori is also
investigated.Comment: submitted to Chao
Collapsing D-branes in one-parameter models and small/large radius duality
We finalize the study of collapsing D-branes in one-parameter models by
completing the analysis of the associated hypergeometric hierarchy. This brings
further evidence that the phenomenon of collapsing 6-branes at the mirror of
the `conifold' point in IIA compactifications on one-parameter Calabi-Yau
manifolds is generic. It also completes the reduction of the study of higher
periods in one-parameter models to a few families which display characteristic
behaviour. One of the models we consider displays an exotic form of small-large
radius duality, which is a consequence of an ``accidental'' discrete symmetry
of its moduli space. We discuss the implementation of this symmetry at the
level of the associated type II string compactification and its action on
D-brane states. We also argue that this model admits two special Lagrangian
fibrations and that the symmetry can be understood as their exchange.Comment: 34 pages, 12 figure
Lifting of the Vlasov-Maxwell Bracket by Lie-transform Method
The Vlasov-Maxwell equations possess a Hamiltonian structure expressed in
terms of a Hamiltonian functional and a functional bracket. In the present
paper, the transformation ("lift") of the Vlasov-Maxwell bracket induced by the
dynamical reduction of single-particle dynamics is investigated when the
reduction is carried out by Lie-transform perturbation methods. The ultimate
goal of this work is to derive explicit Hamiltonian formulations for the
guiding-center and gyrokinetic Vlasov-Maxwell equations that have important
applications in our understanding of turbulent magnetized plasmas. Here, it is
shown that the general form of the reduced Vlasov-Maxwell equations possesses a
Hamiltonian structure defined in terms of a reduced Hamiltonian functional and
a reduced bracket that automatically satisfies the standard bracket properties.Comment: 39 page
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