2,551 research outputs found
Matrix factorizations for nonaffine LG-models
We propose a natural definition of a category of matrix factorizations for
nonaffine Landau-Ginzburg models. For any LG-model we construct a fully
faithful functor from the category of matrix factorizations defined in this way
to the triangulated category of singularities of the corresponding fiber. We
also show that this functor is an equivalence if the total space of the
LG-model is smooth.Comment: 12 pages, minor corrections of TEX fil
Derived categories of Burniat surfaces and exceptional collections
We construct an exceptional collection of maximal possible length
6 on any of the Burniat surfaces with , a 4-dimensional family of
surfaces of general type with . We also calculate the DG algebra of
endomorphisms of this collection and show that the subcategory generated by
this collection is the same for all Burniat surfaces.
The semiorthogonal complement of is an "almost
phantom" category: it has trivial Hochschild homology, and K_0(\mathcal
A)=\bZ_2^6.Comment: 15 pages, 1 figure; further remarks expande
Stability of Landau-Ginzburg branes
We evaluate the ideas of Pi-stability at the Landau-Ginzburg point in moduli
space of compact Calabi-Yau manifolds, using matrix factorizations to B-model
the topological D-brane category. The standard requirement of unitarity at the
IR fixed point is argued to lead to a notion of "R-stability" for matrix
factorizations of quasi-homogeneous LG potentials. The D0-brane on the quintic
at the Landau-Ginzburg point is not obviously unstable. Aiming to relate
R-stability to a moduli space problem, we then study the action of the gauge
group of similarity transformations on matrix factorizations. We define a naive
moment map-like flow on the gauge orbits and use it to study boundary flows in
several examples. Gauge transformations of non-zero degree play an interesting
role for brane-antibrane annihilation. We also give a careful exposition of the
grading of the Landau-Ginzburg category of B-branes, and prove an index theorem
for matrix factorizations.Comment: 46 pages, LaTeX, summary adde
A Scintillating Fiber Hodoscope for a Bremstrahlung Luminosity Monitor at an ElectronPositron Collider
The performance of a scintillating fiber (2mm diameter) position sensitive
detector ( cm active area) for the single bremstrahlung
luminosity monitor at the VEPP-2M electron-positron collider in Novosibirsk,
Russia is described. Custom electronics is triggered by coincident hits in the
X and Y planes of 24 fibers each, and reduces 64 PMT signals to a 10 bit (X,Y)
address. Hits are accumulated (10 kHz) in memory and display (few Hz) the
VEPP-2M collision vertex. Fitting the strongly peaked distribution ( 3-4
mm at 1.6m from the collision vertex of VEPP-2M ) to the expected QED angular
distribution yields a background in agreement with an independent determination
of the VEPP-2M luminosity.Comment: LaTeX with REVTeX style and options: multicol,aps. 8 pages,
postscript figures separate from text. Accepted in Review of Scientific
Instruments (~ Aug 1996
Bound, virtual and resonance -matrix poles from the Schr\"odinger equation
A general method, which we call the potential -matrix pole method, is
developed for obtaining the -matrix pole parameters for bound, virtual and
resonant states based on numerical solutions of the Schr\"odinger equation.
This method is well-known for bound states. In this work we generalize it for
resonant and virtual states, although the corresponding solutions increase
exponentially when . Concrete calculations are performed for the
ground and the first excited states of , the resonance
states (, ), low-lying states of and
, and the subthreshold resonances in the proton-proton system. We
also demonstrate that in the case the broad resonances their energy and width
can be found from the fitting of the experimental phase shifts using the
analytical expression for the elastic scattering -matrix. We compare the
-matrix pole and the -matrix for broad resonance in
Comment: 14 pages, 5 figures (figures 3 and 4 consist of two figures each) and
4 table
Semiorthogonal decompositions of derived categories of equivariant coherent sheaves
Let X be an algebraic variety with an action of an algebraic group G. Suppose
X has a full exceptional collection of sheaves, and these sheaves are invariant
under the action of the group. We construct a semiorthogonal decomposition of
bounded derived category of G-equivariant coherent sheaves on X into
components, equivalent to derived categories of twisted representations of the
group. If the group is finite or reductive over the algebraically closed field
of zero characteristic, this gives a full exceptional collection in the derived
equivariant category. We apply our results to particular varieties such as
projective spaces, quadrics, Grassmanians and Del Pezzo surfaces.Comment: 28 pages, uses XY-pi
More on general -brane solutions
Recently it was found that the complete integration of the
Einstein-dilaton-antisymmetric form equations depending on one variable and
describing static singly charged -branes leads to two and only two classes
of solutions: the standard asymptotically flat black -brane and the
asymptotically non-flat -brane approaching the linear dilaton background at
spatial infinity. Here we analyze this issue in more details and generalize the
corresponding uniqueness argument to the case of partially delocalized branes.
We also consider the special case of codimension one and find, in addition to
the standard domain wall, the black wall solution. Explicit relations between
our solutions and some recently found -brane solutions ``with extra
parameters'' are presented.Comment: 29 pages, 2 figure
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