1,699 research outputs found
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
The economic characteristic of products and services in the sphere of communications and informatization
The basic economic characteristics of products and services in the sphere of communication and informatization are considered in the article
Evolution equation of quantum tomograms for a driven oscillator in the case of the general linear quantization
The symlectic quantum tomography for the general linear quantization is
introduced. Using the approach based upon the Wigner function techniques the
evolution equation of quantum tomograms is derived for a parametric driven
oscillator.Comment: 11 page
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
Deformation theory of objects in homotopy and derived categories II: pro-representability of the deformation functor
This is the second paper in a series. In part I we developed deformation
theory of objects in homotopy and derived categories of DG categories. Here we
extend these (derived) deformation functors to an appropriate bicategory of
artinian DG algebras and prove that these extended functors are
pro-representable in a strong sense.Comment: Alexander Efimov is a new co-author of this paper. New material was
added: A_{\infty}-structures, Maurer-Cartan theory for A_{\infty}-algebras.
This allows us to strengthen our main results on the pro-representability of
pseudo-functors coDEF_{-} and DEF_{-}. We also obtain an equivalence between
homotopy and derived deformation functors under weaker hypothese
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
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