2,626 research outputs found

    Counting charged massless states in the (0,2) heterotic CFT/geometry connection

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    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

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    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 ×\times log n ×\times 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 ×\times log n ×\times 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

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    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

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    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

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    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

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    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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