1,441 research outputs found
Topological A-Type Models with Flux
We study deformations of the A-model in the presence of fluxes, by which we
mean rank-three tensors with antisymmetrized upper/lower indices, using the
AKSZ construction. Generically these are topological membrane models, and we
show that the fluxes are related to deformations of the Courant bracket which
generalize the twist by a closed 3-from , in the sense that satisfying the
AKSZ master equation implies the integrability conditions for an almost
generalized complex structure with respect to the deformed Courant bracket. In
addition, the master equation imposes conditions on the fluxes that generalize
. The membrane model can be defined on a large class of - and -structure manifolds, including geometries inspired by
supersymmetric -models with additional supersymmetries due to almost
complex (but not necessarily complex) structures in the target space.
Furthermore, we show that the model can be defined on three particular
half-flat manifolds related to the Iwasawa manifold.
When only -flux is turned on it is possible to obtain a topological string
model, which we do for the case of a Calabi-Yau with a closed 3-form turned on.
The simplest deformation from the A-model is due to the
component of a non-trivial -field. The model is generically no longer
evaluated on holomorphic maps and defines new topological invariants.
Deformations due to -flux can be more radical, completely preventing
auxiliary fields from being integrated out.Comment: 30 pages. v2: Improved Version. References added. v3: Minor changes,
published in JHE
Relating harmonic and projective descriptions of N=2 nonlinear sigma models
Recent papers have established the relationship between projective superspace
and a complexified version of harmonic superspace. We extend this construction
to the case of general nonlinear sigma models in both frameworks. Using an
analogy with Hamiltonian mechanics, we demonstrate how the Hamiltonian
structure of the harmonic action and the symplectic structure of the projective
action naturally arise from a single unifying action on a complexified version
of harmonic superspace. This links the harmonic and projective descriptions of
hyperkahler target spaces. For the two examples of Taub-NUT and Eguchi-Hanson,
we show how to derive the projective superspace solutions from the harmonic
superspace solutions.Comment: 25 pages; v3: typo fixed in eq (1.36
Covariant path integral for chiral p-forms
The covariant path integral for chiral bosons obtained by McClain, Wu and Yu
is generalized to chiral p-forms. In order to handle the reducibility of the
gauge transformations associated with the chiral p-forms and with the new
variables (in infinite number) that must be added to eliminate the second class
constraints, the field-antifield formalism is used.Comment: revtex, 9 pages, submitted to Physical Review
On the Metric Dimension of Cartesian Products of Graphs
A set S of vertices in a graph G resolves G if every vertex is uniquely
determined by its vector of distances to the vertices in S. The metric
dimension of G is the minimum cardinality of a resolving set of G. This paper
studies the metric dimension of cartesian products G*H. We prove that the
metric dimension of G*G is tied in a strong sense to the minimum order of a
so-called doubly resolving set in G. Using bounds on the order of doubly
resolving sets, we establish bounds on G*H for many examples of G and H. One of
our main results is a family of graphs G with bounded metric dimension for
which the metric dimension of G*G is unbounded
N = 2 supersymmetric sigma-models and duality
For two families of four-dimensional off-shell N = 2 supersymmetric nonlinear
sigma-models constructed originally in projective superspace, we develop their
formulation in terms of N = 1 chiral superfields. Specifically, these theories
are: (i) sigma-models on cotangent bundles T*M of arbitrary real analytic
Kaehler manifolds M; (ii) general superconformal sigma-models described by
weight-one polar supermultiplets. Using superspace techniques, we obtain a
universal expression for the holomorphic symplectic two-form \omega^{(2,0)}
which determines the second supersymmetry transformation and is associated with
the two complex structures of the hyperkaehler space T*M that are complimentary
to the one induced from M. This two-form is shown to coincide with the
canonical holomorphic symplectic structure. In the case (ii), we demonstrate
that \omega^{(2,0)} and the homothetic conformal Killing vector determine the
explicit form of the superconformal transformations. At the heart of our
construction is the duality (generalized Legendre transform) between off-shell
N = 2 supersymmetric nonlinear sigma-models and their on-shell N = 1 chiral
realizations. We finally present the most general N = 2 superconformal
nonlinear sigma-model formulated in terms of N = 1 chiral superfields. The
approach developed can naturally be generalized in order to describe 5D and 6D
superconformal nonlinear sigma-models in 4D N = 1 superspace.Comment: 31 pages, no figures; V2: reference and comments added, typos
corrected; V3: more typos corrected, published versio
Six-dimensional Supergravity and Projective Superfields
We propose a superspace formulation of N=(1,0) conformal supergravity in six
dimensions. The corresponding superspace constraints are invariant under
super-Weyl transformations generated by a real scalar parameter. The known
variant Weyl super-multiplet is recovered by coupling the geometry to a
super-3-form tensor multiplet. Isotwistor variables are introduced and used to
define projective superfields. We formulate a locally supersymmetric and
super-Weyl invariant action principle in projective superspace. Some families
of dynamical supergravity-matter systems are presented.Comment: 39 pages; v3: some modifications in section 2; equations (2.3),
(2.14b), (2.16) and (2.17) correcte
D-instantons and twistors: some exact results
We present some results on instanton corrections to the hypermultiplet moduli
space in Calabi-Yau compactifications of Type II string theories. Previously,
using twistor methods, only a class of D-instantons (D2-instantons wrapping
A-cycles) was incorporated exactly and the rest was treated only linearly. We
go beyond the linear approximation and give a set of holomorphic functions
which, through a known procedure, capture the effect of D-instantons at all
orders. Moreover, we show that for a sector where all instanton charges have
vanishing symplectic invariant scalar product, the hypermultiplet metric can be
computed explicitly.Comment: 32 pages, 3 figures, uses JHEP3.cls; some changes in section 3.3.3;
corrected formula for the contact potentia
Super Calabi-Yau's and Special Lagrangians
We apply mirror symmetry to the super Calabi-Yau manifold CP^{(n|n+1)} and
show that the mirror can be recast in a form which depends only on the
superdimension and which is reminiscent of a generalized conifold. We discuss
its geometrical properties in comparison to the familiar conifold geometry. In
the second part of the paper examples of special-Lagrangian submanifolds are
constructed for a class of super Calabi-Yau's. We finally comment on their
infinitesimal deformations.Comment: 20 pages, no figures, latex; v2: references added; v3: minor
clarifications added, version published in JHE
Classical phase space and statistical mechanics of identical particles
Starting from the quantum theory of identical particles, we show how to
define a classical mechanics that retains information about the quantum
statistics. We consider two examples of relevance for the quantum Hall effect:
identical particles in the lowest Landau level, and vortices in the
Chern-Simons Ginzburg-Landau model. In both cases the resulting {\em classical}
statistical mechanics is shown to be a nontrivial classical limit of Haldane's
exclusion statistics.Comment: 40 pages, Late
What counts as ârespondingâ? Contingency on previous speaker contribution as a feature of interactional competence
The ability to interact with others has gained recognition as part of the L2 speaking construct in the assessment literature and in high- and low-stakes speaking assessments. This paper first presents a review of the literature on interactional competence (IC) in L2 learning and assessment. It then discusses a particular feature â producing responses contingent on previous speaker contribution â that emerged as a de facto construct feature of IC oriented to by both candidates and examiners within the school-based group speaking assessment in the Hong Kong Diploma of Secondary Education (HKDSE) English Language Examination. Previous studies have, similarly, argued for the importance of âresponding toâ or linking oneâs own talk to previous speakersâ contributions as a way of demonstrating comprehension of co-participantsâ talk. However, what counts as such a response has yet to be explored systematically. This paper presents a conversation analytic study of the candidate discourse in the assessed group interactions, identifying three conversational actions through which student-candidates construct contingent responses to co-participants. The thick description about the nature of contingent responses lays the groundwork for further empirical investigations on the relevance of this IC feature and its proficiency implications
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