2,510 research outputs found
Crisp and fuzzy motif and arrangement symmetries in composite geometric figures
AbstractThe notions of motif and arrangement symmetries within composite geometric figures are defined. The relationships between these types of symmetry and the symmetry of the whole figure are clarified by making use of the crystallographic concepts of site symmetry and direction symmetry. From this, it has been deduced that a figure with arbitrary symmetry can be assembled from motifs of likewise arbitrary symmetries. If a motif with symmetry GM is placed on a site having the site symmetry GS ⊆ GM, its contribution to the figure symmetry G is only a subgroup G*MO of its direction symmetry GMO where GS = G*MO ⊆ GMO ⊆ GM. Supernumerary symmetry elements of the motif give rise to intermediate or latent symmetries of the figure. A consequent decomposition of a geometric figure into its constituent points reveals that a large part of the O(n) symmetry of every single point is lost when assembling these points to build up the figure. All “lost” symmetries can, however, be detected as intermediate symmetries of this figure. They can be displayed as fuzzy symmetry landscapes and symmetry profiles for a given figure showing all crisp and intermediate symmetries of interest
Quantum Matrix Models for Simple Current Orbifolds
An algebraic formulation of the stringy geometry on simple current orbifolds
of the WZW models of type A_N is developed within the framework of Reflection
Equation Algebras, REA_q(A_N). It is demonstrated that REA_q(A_N) has the same
set of outer automorphisms as the corresponding current algebra A^{(1)}_N which
is crucial for the orbifold construction. The CFT monodromy charge is naturally
identified within the algebraic framework. The ensuing orbifold matrix models
are shown to yield results on brane tensions and the algebra of functions in
agreement with the exact BCFT data.Comment: 31 pages, LaTeX; typos corrected, new elements added, the contents
restructure
Classification and Quantum Moduli Space of D-branes in Group Manifolds
We study the classification of D-branes in all compact Lie groups including
non-simply-laced ones. We also discuss the global structure of the quantum
moduli space of the D-branes. D-branes are classified according to their
positions in the maximal torus. We describe rank 2 cases, namely , ,
, explicitly and construct all the D-branes in , , by the
method of iterative deletion in the Dynkin diagram. The discussion of moduli
space involves global issues that can be treated in terms of the exact homotopy
sequence and various lattices. We also show that singular D-branes can exist at
quantum mechanical level.Comment: latex2e, 13 pages, 3 figures. v4: A reference added. Version to
appear in Phys. Lett.
Hypermatrix factors for string and membrane junctions
The adjoint representations of the Lie algebras of the classical groups
SU(n), SO(n), and Sp(n) are, respectively, tensor, antisymmetric, and symmetric
products of two vector spaces, and hence are matrix representations. We
consider the analogous products of three vector spaces and study when they
appear as summands in Lie algebra decompositions. The Z3-grading of the
exceptional Lie algebras provide such summands and provides representations of
classical groups on hypermatrices. The main natural application is a formal
study of three-junctions of strings and membranes. Generalizations are also
considered.Comment: 25 pages, 4 figures, presentation improved, minor correction
Open Strings in Simple Current Orbifolds
We study branes and open strings in a large class of orbifolds of a curved
background using microscopic techniques of boundary conformal field theory. In
particular, we obtain factorizing operator product expansions of open string
vertex operators for such branes. Applications include branes in Z2 orbifolds
of the SU(2) WZW model and in the D-series of unitary minimal models considered
previously by Runkel.Comment: Latex, 1 figur
SciTech News Volume 71, No. 2 (2017)
Columns and Reports From the Editor 3
Division News Science-Technology Division 5 Chemistry Division 8 Engineering Division 9 Aerospace Section of the Engineering Division 12 Architecture, Building Engineering, Construction and Design Section of the Engineering Division 14
Reviews Sci-Tech Book News Reviews 16
Advertisements IEEE
- …