2,626 research outputs found
Counting charged massless states in the (0,2) heterotic CFT/geometry connection
We use simple current techniques and their relation to orbifolds with
discrete torsion for studying the (0,2) CFT/geometry duality with non-rational
internal N=2 SCFTs. Explicit formulas for the charged spectra of heterotic
SO(10) GUT models are computed in terms of their extended Poincar\'{e}
polynomials and the complementary Poincar\'{e} polynomial which can be computed
in terms of the elliptic genera. While non-BPS states contribute to the charged
spectrum, their contributions can be determined also for non-rational cases.
For model building, with generalizations to SU(5) and SM gauge groups, one can
take advantage of the large class of Landau-Ginzburg orbifold examples.Comment: 51 pages. Acknowledgments update
Fast integer multiplication using generalized Fermat primes
For almost 35 years, Sch{\"o}nhage-Strassen's algorithm has been the fastest
algorithm known for multiplying integers, with a time complexity O(n
log n log log n) for multiplying n-bit inputs. In 2007, F{\"u}rer
proved that there exists K > 1 and an algorithm performing this operation in
O(n log n K log n). Recent work by Harvey, van der Hoeven,
and Lecerf showed that this complexity estimate can be improved in order to get
K = 8, and conjecturally K = 4. Using an alternative algorithm, which relies on
arithmetic modulo generalized Fermat primes, we obtain conjecturally the same
result K = 4 via a careful complexity analysis in the deterministic multitape
Turing model
On Smarandache's form of the individual Fermat-Euler theorem
In the paper it is shown how a form of the classical FERMAT-EULER Theorem discovered by F. SMARANDACHE fits into the generalizations found by S.SCHWARZ, M.LASSAK and the author. Then we show how SMARANDACHE'S
algorithm can be used to effective computations of the so called group membership
Complex Multiplication Symmetry of Black Hole Attractors
We show how Moore's observation, in the context of toroidal compactifications
in type IIB string theory, concerning the complex multiplication structure of
black hole attractor varieties, can be generalized to Calabi-Yau
compactifications with finite fundamental groups. This generalization leads to
an alternative general framework in terms of motives associated to a Calabi-Yau
variety in which it is possible to address the arithmetic nature of the
attractor varieties in a universal way via Deligne's period conjecture.Comment: 28 page
Complex Multiplication of Exactly Solvable Calabi-Yau Varieties
We propose a conceptual framework that leads to an abstract characterization
for the exact solvability of Calabi-Yau varieties in terms of abelian varieties
with complex multiplication. The abelian manifolds are derived from the
cohomology of the Calabi-Yau manifold, and the conformal field theoretic
quantities of the underlying string emerge from the number theoretic structure
induced on the varieties by the complex multiplication symmetry. The geometric
structure that provides a conceptual interpretation of the relation between
geometry and the conformal field theory is discrete, and turns out to be given
by the torsion points on the abelian varieties.Comment: 44 page
Black Hole Attractor Varieties and Complex Multiplication
Black holes in string theory compactified on Calabi-Yau varieties a priori
might be expected to have moduli dependent features. For example the entropy of
the black hole might be expected to depend on the complex structure of the
manifold. This would be inconsistent with known properties of black holes.
Supersymmetric black holes appear to evade this inconsistency by having moduli
fields that flow to fixed points in the moduli space that depend only on the
charges of the black hole. Moore observed in the case of compactifications with
elliptic curve factors that these fixed points are arithmetic, corresponding to
curves with complex multiplication. The main goal of this talk is to explore
the possibility of generalizing such a characterization to Calabi-Yau varieties
with finite fundamental groups.Comment: 21 page
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