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

Scaling behavior of observables as a model characteristic in multifield inflation

One of the fundamental questions in inflation is how to characterize the structure of different types of models in the field theoretic landscape. Proposals in this direction include attempts to directly characterize the formal structure of the theory by considering complexity measures of the potentials. An alternative intrinsic approach is to focus on the behavior of the observables that result from different models and to ask whether their behavior differs among models. This type of analysis can be applied even to nontrivial multifield theories where a natural measure of the complexity of the model is not obvious and the analytical evaluation of the observables is often impossible. In such cases one may still compute these observables numerically and investigate their behavior. One interesting case is when observables show a scaling behavior, in which case theories can be characterized in terms of their scaling amplitudes and exponents. Generically, models have nontrivial parameter spaces, leading to exponents that are functions of these parameters. In such cases we consider an iterative procedure to determine whether the exponent functions in turn lead to a scaling behavior. We show that modular inflation models can be characterized by families of simple scaling laws and that the scaling exponents that arise in this way in turn show a scaling law in dependence of these varying energy scales.Comment: 20 pages, 6 figure

Landau-Ginzburg Vacua of String, M- and F-Theory at c=12

Theories in more than ten dimensions play an important role in understanding nonperturbative aspects of string theory. Consistent compactifications of such theories can be constructed via Calabi-Yau fourfolds. These models can be analyzed particularly efficiently in the Landau-Ginzburg phase of the linear sigma model, when available. In the present paper we focus on those sigma models which have both a Landau-Ginzburg phase and a geometric phase described by hypersurfaces in weighted projective five-space. We describe some of the pertinent properties of these models, such as the cohomology, the connectivity of the resulting moduli space, and mirror symmetry among the 1,100,055 configurations which we have constructed.Comment: LaTeX, 33 pages, 10 PostScript figures using epsfig and psfi

Observation and Properties of the X(3872) Decaying to J/ψπ+π− in p¯p Collisions at √s = 1.96 TeV

We report the observation of the X(3872) in the J/psi pi+pi- channel, with J/psi decaying to mu+mu- in p-p(bar) collisions at sqrt(s) = 1.96 TeV. Using approximately 230 pb^-1 of data collected with the Run II D0 detector, we observe 522 +/- 100 X(3872) candidates. The mass difference between the X(3872) state and the J/psi is measured to be 774.9 +/- 3.1 (stat.) +/- 3.0 (syst.) MeV/c^2. We have investigated the production and decay characteristics of the X(3872), and find them to be similar to those of the psi(2S) state

Unification of M- and F- Theory Calabi-Yau Fourfold Vacua

We consider splitting type phase transitions between Calabi-Yau fourfolds. These transitions generalize previously known types of conifold transitions between threefolds. Similar to conifold configurations the singular varieties mediating the transitions between fourfolds connect moduli spaces of different dimensions, describing ground states in M- and F-theory with different numbers of massless modes as well as different numbers of cycles to wrap various p-branes around. The web of Calabi-Yau fourfolds obtained in this way contains the class of all complete intersection manifolds embedded in products of ordinary projective spaces, but extends also to weighted configurations. It follows from this that for some of the fourfold transitions vacua with vanishing superpotential are connected to ground states with nonzero superpotential.Comment: plain TeX, 22p

String Modular Phases in Calabi-Yau Families

We investigate the structure of singular Calabi-Yau varieties in moduli spaces that contain a Brieskorn-Pham point. Our main tool is a construction of families of deformed motives over the parameter space. We analyze these motives for general fibers and explicitly compute the $L-$series for singular fibers for several families. We find that the resulting motivic $L-$functions agree with the $L-$series of modular forms whose weight depends both on the rank of the motive and the degree of the degeneration of the variety. Surprisingly, these motivic $L-$functions are identical in several cases to $L-$series derived from weighted Fermat hypersurfaces. This shows that singular Calabi-Yau spaces of non-conifold type can admit a string worldsheet interpretation, much like rational theories, and that the corresponding irrational conformal field theories inherit information from the Gepner conformal field theory of the weighted Fermat fiber of the family. These results suggest that phase transitions via non-conifold configurations are physically plausible. In the case of severe degenerations we find a dimensional transmutation of the motives. This suggests further that singular configurations with non-conifold singularities may facilitate transitions between Calabi-Yau varieties of different dimensions.Comment: 34 page

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

Geometric Kac-Moody Modularity

It is shown how the arithmetic structure of algebraic curves encoded in the Hasse-Weil L-function can be related to affine Kac-Moody algebras. This result is useful in relating the arithmetic geometry of Calabi-Yau varieties to the underlying exactly solvable theory. In the case of the genus three Fermat curve we identify the Hasse-Weil L-function with the Mellin transform of the twist of a number theoretic modular form derived from the string function of a non-twisted affine Lie algebra. The twist character is associated to the number field of quantum dimensions of the underlying conformal field theory