1,130 research outputs found
The Breakdown of Topology at Small Scales
We discuss how a topology (the Zariski topology) on a space can appear to
break down at small distances due to D-brane decay. The mechanism proposed
coincides perfectly with the phase picture of Calabi-Yau moduli spaces. The
topology breaks down as one approaches non-geometric phases. This picture is
not without its limitations, which are also discussed.Comment: 12 pages, 2 figure
Quivers from Matrix Factorizations
We discuss how matrix factorizations offer a practical method of computing
the quiver and associated superpotential for a hypersurface singularity. This
method also yields explicit geometrical interpretations of D-branes (i.e.,
quiver representations) on a resolution given in terms of Grassmannians. As an
example we analyze some non-toric singularities which are resolved by a single
CP1 but have "length" greater than one. These examples have a much richer
structure than conifolds. A picture is proposed that relates matrix
factorizations in Landau-Ginzburg theories to the way that matrix
factorizations are used in this paper to perform noncommutative resolutions.Comment: 33 pages, (minor changes
Twistfield Perturbations of Vertex Operators in the Z_2-Orbifold Model
We apply Kadanoff's theory of marginal deformations of conformal field
theories to twistfield deformations of Z_2 orbifold models in K3 moduli space.
These deformations lead away from the Z_2 orbifold sub-moduli-space and hence
help to explore conformal field theories which have not yet been understood. In
particular, we calculate the deformation of the conformal dimensions of vertex
operators for p^2<1 in second order perturbation theory.Comment: Latex2e, 19 pages, 1 figur
On the Matrix Description of Calabi-Yau Compactifications
We point out that the matrix description of M-theory compactified on
Calabi-Yau threefolds is in many respects simpler than the matrix description
of a compactification. This is largely because of the differences between
D6 branes wrapped on Calabi-Yau threefolds and D6 branes wrapped on six-tori.
In particular, if we define the matrix theory following the prescription of Sen
and Seiberg, we find that the remaining degrees of freedom are decoupled from
gravity.Comment: 12 pages, harvmac big; comment on 4d N=1 theories change
Topological Field Theory and Rational Curves
We analyze the superstring propagating on a Calabi-Yau threefold. This theory
naturally leads to the consideration of Witten's topological non-linear
sigma-model and the structure of rational curves on the Calabi-Yau manifold. We
study in detail the case of the world-sheet of the string being mapped to a
multiple cover of an isolated rational curve and we show that a natural
compactification of the moduli space of such a multiple cover leads to a
formula in agreement with a conjecture by Candelas, de la Ossa, Green and
Parkes.Comment: 20 page
Kaluza-Klein electrically charged black branes in M-theory
We present a class of Kaluza-Klein electrically charged black p-brane
solutions of ten-dimensional, type IIA superstring theory. Uplifting to eleven
dimensions these solutions are studied in the context of M-theory. They can be
interpreted either as a p+1 extended object trapped around the eleventh
dimension along which momentum is flowing or as a boost of the following
backgrounds: the Schwarzschild black (p+1)-brane or the product of the
(10-p)-dimensional Euclidean Schwarzschild manifold with the (p+1)-dimensional
Minkowski spacetime.Comment: 16 pages, uses latex and epsf macro, figures include
Heterotic-Type II duality in the hypermultiplet sector
We revisit the duality between heterotic string theory compactified on K3 x
T^2 and type IIA compactified on a Calabi-Yau threefold X in the hypermultiplet
sector. We derive an explicit map between the field variables of the respective
moduli spaces at the level of the classical effective actions. We determine the
parametrization of the K3 moduli space consistent with the Ferrara-Sabharwal
form. From the expression of the holomorphic prepotential we are led to
conjecture that both X and its mirror must be K3 fibrations in order for the
type IIA theory to have an heterotic dual. We then focus on the region of the
moduli space where the metric is expressed in terms of a prepotential on both
sides of the duality. Applying the duality we derive the heterotic
hypermultiplet metric for a gauge bundle which is reduced to 24 point-like
instantons. This result is confirmed by using the duality between the heterotic
theory on T^3 and M-theory on K3. We finally study the hyper-Kaehler metric on
the moduli space of an SU(2) bundle on K3.Comment: 27 pages; references added, typos correcte
Defect Perturbations in Landau-Ginzburg Models
Perturbations of B-type defects in Landau-Ginzburg models are considered. In
particular, the effect of perturbations of defects on their fusion is analyzed
in the framework of matrix factorizations. As an application, it is discussed
how fusion with perturbed defects induces perturbations on boundary conditions.
It is shown that in some classes of models all boundary perturbations can be
obtained in this way. Moreover, a universal class of perturbed defects is
constructed, whose fusion under certain conditions obey braid relations. The
functors obtained by fusing these defects with boundary conditions are twist
functors as introduced in the work of Seidel and Thomas.Comment: 46 page
Global Properties of Topological String Amplitudes and Orbifold Invariants
We derive topological string amplitudes on local Calabi-Yau manifolds in
terms of polynomials in finitely many generators of special functions. These
objects are defined globally in the moduli space and lead to a description of
mirror symmetry at any point in the moduli space. Holomorphic ambiguities of
the anomaly equations are fixed by global information obtained from boundary
conditions at few special divisors in the moduli space. As an illustration we
compute higher genus orbifold Gromov-Witten invariants for C^3/Z_3 and C^3/Z_4.Comment: 34 pages, 3 figure
Gauging and symplectic blowing up in nonlinear sigma-models: I. point singularities
In this paper a two dimensional non-linear sigma model with a general
symplectic manifold with isometry as target space is used to study symplectic
blowing up of a point singularity on the zero level set of the moment map
associated with a quasi-free Hamiltonian action. We discuss in general the
relation between symplectic reduction and gauging of the symplectic isometries
of the sigma model action. In the case of singular reduction, gauging has the
same effect as blowing up the singular point by a small amount. Using the
exponential mapping of the underlying metric, we are able to construct
symplectic diffeomorphisms needed to glue the blow-up to the global reduced
space which is regular, thus providing a transition from one symplectic sigma
model to another one free of singularities.Comment: 32 pages, LaTex, THEP 93/24 (corrected and expanded(about 5 pages)
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