2,316 research outputs found
Reflection groups in hyperbolic spaces and the denominator formula for Lorentzian Kac--Moody Lie algebras
This is a continuation of our "Lecture on Kac--Moody Lie algebras of the
arithmetic type" \cite{25}.
We consider hyperbolic (i.e. signature ) integral symmetric bilinear
form (i.e. hyperbolic lattice), reflection group
, fundamental polyhedron \Cal M of and an acceptable
(corresponding to twisting coefficients) set P({\Cal M})\subset M of vectors
orthogonal to faces of \Cal M (simple roots). One can construct the
corresponding Lorentzian Kac--Moody Lie algebra {\goth g}={\goth
g}^{\prime\prime}(A(S,W,P({\Cal M}))) which is graded by .
We show that \goth g has good behavior of imaginary roots, its denominator
formula is defined in a natural domain and has good automorphic properties if
and only if \goth g has so called {\it restricted arithmetic type}. We show
that every finitely generated (i.e. P({\Cal M}) is finite) algebra {\goth
g}^{\prime\prime}(A(S,W_1,P({\Cal M}_1))) may be embedded to {\goth
g}^{\prime\prime}(A(S,W,P({\Cal M}))) of the restricted arithmetic type. Thus,
Lorentzian Kac--Moody Lie algebras of the restricted arithmetic type is a
natural class to study.
Lorentzian Kac--Moody Lie algebras of the restricted arithmetic type have the
best automorphic properties for the denominator function if they have {\it a
lattice Weyl vector }. Lorentzian Kac--Moody Lie algebras of the
restricted arithmetic type with generalized lattice Weyl vector are
called {\it elliptic}Comment: Some corrections in Sects. 2.1, 2.2 were done. They don't reflect on
results and ideas. 31 pages, no figures. AMSTe
Generation of Plasma in Low-Pressure Discharge
A hydrodynamic model of plasma has been developed, which takes into account both secondary and primary electrons. It has been shown that a solution with a plasma potential higher than the anode potential is possible if the ionization frequency is higher than some critical value. At lower ionization frequencies, it is possible to obtain a solution with a plasma potential below the anode potential. © 2021 Institute of Physics Publishing. All rights reserved
Formation of conserved charge at the de Sitter space
The article considers a new mechanism of charge accumulation in the early
Universe in theories with compact extra dimensions. The relaxation processes in
the extra space metric that take place during its formation lead to the
establishment of symmetrical extra space configuration. As a result, the
initial accumulation of the number associated with the symmetry occurs. We
demonstrate this mechanism using a simple example of a two-dimensional
apple-like extra space metric with -symmetry. The conceptual idea of the
mechanism can be used to develop a model for the production of the baryon or
lepton number in the early Universe.Comment: 9 pages, 3 figure
On Type IIB Vacua With Varying Coupling Constant
We describe type IIB compactifications with varying coupling constant in
d=6,7,8,9 dimensions, where part of the ten-dimensional SL(2,Z) symmetry is
broken by a background with Gamma_0(n) or Gamma(n) monodromy for n=2,3,4. This
extends the known class of F-theory vacua to theories which are dual to
heterotic compactifications with reduced rank. On compactifying on a further
torus, we obtain a description of the heterotic moduli space of G bundles over
elliptically fibered manifolds without vector structure in terms of complex
geometries.Comment: 32 pages, 5 eps figure
K3-fibered Calabi-Yau threefolds I, the twist map
A construction of Calabi-Yaus as quotients of products of lower-dimensional
spaces in the context of weighted hypersurfaces is discussed, including
desingularisation. The construction leads to Calabi-Yaus which have a fiber
structure, in particular one case has K3 surfaces as fibers. These Calabi-Yaus
are of some interest in connection with Type II -heterotic string dualities in
dimension 4. A section at the end of the paper summarises this for the
non-expert mathematician.Comment: 31 pages LaTeX, 11pt, 2 figures. To appear in International Journal
of Mathematics. On the web at
http://personal-homepages.mis.mpg.de/bhunt/preprints.html , #
2-elementary subgroups of the space Cremona group
We give a sharp bound for orders of elementary abelian 2-groups of birational
automorphisms of rationally connected threefolds
Families of Quintic Calabi-Yau 3-Folds with Discrete Symmetries
At special loci in their moduli spaces, Calabi-Yau manifolds are endowed with
discrete symmetries. Over the years, such spaces have been intensely studied
and have found a variety of important applications. As string compactifications
they are phenomenologically favored, and considerably simplify many important
calculations. Mathematically, they provided the framework for the first
construction of mirror manifolds, and the resulting rational curve counts.
Thus, it is of significant interest to investigate such manifolds further. In
this paper, we consider several unexplored loci within familiar families of
Calabi-Yau hypersurfaces that have large but unexpected discrete symmetry
groups. By deriving, correcting, and generalizing a technique similar to that
of Candelas, de la Ossa and Rodriguez-Villegas, we find a calculationally
tractable means of finding the Picard-Fuchs equations satisfied by the periods
of all 3-forms in these families. To provide a modest point of comparison, we
then briefly investigate the relation between the size of the symmetry group
along these loci and the number of nonzero Yukawa couplings. We include an
introductory exposition of the mathematics involved, intended to be accessible
to physicists, in order to make the discussion self-contained.Comment: 54 pages, 3 figure
M-Theory on (K3 X S^1)/Z_2
We analyze -theory compactified on where the
changes the sign of the three form gauge field, acts on as a parity
transformation and on K3 as an involution with eight fixed points preserving
SU(2) holonomy. At a generic point in the moduli space the resulting theory has
as its low energy limit N=1 supergravity theory in six dimensions with eight
vector, nine tensor and twenty hypermultiplets. The gauge symmetry can be
enhanced (e.g. to ) at special points in the moduli space. At other
special points in the moduli space tensionless strings appear in the theory.Comment: LaTeX file, 11 page
Period- and mirror-maps for the quartic K3
We study in detail mirror symmetry for the quartic K3 surface in P3 and the
mirror family obtained by the orbifold construction. As explained by Aspinwall
and Morrison, mirror symmetry for K3 surfaces can be entirely described in
terms of Hodge structures. (1) We give an explicit computation of the Hodge
structures and period maps for these families of K3 surfaces. (2) We identify a
mirror map, i.e. an isomorphism between the complex and symplectic deformation
parameters, and explicit isomorphisms between the Hodge structures at these
points. (3) We show compatibility of our mirror map with the one defined by
Morrison near the point of maximal unipotent monodromy. Our results rely on
earlier work by Narumiyah-Shiga, Dolgachev and Nagura-Sugiyama.Comment: 29 pages, 3 figure
State-of-the-art of historical earthquake research in Fennoscandia and the Baltic Republics
We review historical earthquake research in Northern Europe. 'Historical' is defined as being identical with seismic events occurring in the pre-instrumental and early instrumental periods between 1073 and the mid-1960s. The first seismographs in this region were installed in Uppsala, Sweden and Bergen, Norway in 1904-1905, but these mechanical pendulum instruments were broad band and amplification factors were modest at around 500. Until the 1960s few modern
short period electromagnetic seismographs were deployed. Scientific earthquake studies in this region began during the first decades of the 1800s, while the systematic use of macroseismic questionnaires commenced at the end of that
century. Basic research efforts have vigorously been pursued from the 1970s onwards because of the mandatory seismic
risk studies for commissioning nuclear power plants in Sweden, Finland, NW Russia, Kola and installations of huge oil
platforms in the North Sea. The most comprehensive earthquake database currently available for Northern Europe is the
FENCAT catalogue covering about six centuries and representing the accumulation of work conducted by many scientists
during the last 200 years. This catalogue is given in parametric form, while original macroseismic observations and intensity
maps for the largest earthquakes can be found in various national publications, often in local languages. No database
giving intensity data points exists in computerized form for the region. The FENCAT catalogue still contains some
spurious events of various kinds but more serious are some recent claims that some of the presumed largest historical earthquakes have been assigned too large magnitude values, which would have implications for earthquake hazard levels implemented in national building codes. We discuss future cooperative measures such as establishing macroseismic data archives as a means for promoting further research on historical earthquakes in Northern Europe
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