David R. Morrison

Kepler Planet-Detection Mission: Introduction and First Results

Detecting Distant Planets More than 400 planets have been detected outside the solar system, most of which have masses similar to that of the gas giant planet, Jupiter. Borucki et al. (p. 977, published online 7 January) summarize the planetary findings derived from the first six weeks of observations with the Kepler mission whose objective is to search for and determine the frequency of Earth-like planets in the habitable zones of other stars. The results include the detection of five new exoplanets, which confirm the existence of planets with densities substantially lower than those predicted for gas giant planets. Initial observations confirm the existence of planets with densities lower than those predicted for gas giant planets. The Kepler mission was designed to determine the frequency of Earth-sized planets in and near the habitable zone of Sun-like stars. The habitable zone is the region where planetary temperatures are suitable for water to exist on a planet’s surface. During the first 6 weeks of observations, Kepler monitored 156,000 stars, and five new exoplanets with sizes between 0.37 and 1.6 Jupiter radii and orbital periods from 3.2 to 4.9 days were discovered. The density of the Neptune-sized Kepler-4b is similar to that of Neptune and GJ 436b, even though the irradiation level is 800,000 times higher. Kepler-7b is one of the lowest-density planets (~0.17 gram per cubic centimeter) yet detected. Kepler-5b, -6b, and -8b confirm the existence of planets with densities lower than those predicted for gas giant planets.

Compactifications of F-theory on Calabi-Yau threefolds (II)

Abstract We continue our study of compactifications of F-theory on Calabi-Yau threefolds. We gain more insight into F-theory duals of heterotic strings and provide a recipe for building F-theory duals for arbitrary heterotic compactifications on elliptically fibered manifolds. As a byproduct we find that string/string duality in six dimensions gets mapped to fiber/base exchange in F-theory. We also construct a number of new N = 1, d = 6 examples of F-theory vacua and study transitions among them. We find that some of these transition points correspond upon further compactification to 4 dimensions to transitions through analogues of Argyres-Douglas points of N = 2 moduli. A key idea in these transitions is the notion of classifying (0,4) fivebranes of heterotic strings.

Geometric singularities and enhanced gauge symmetries

Abstract Using “Tates algorithm,” we identify loci in the moduli of F-theory compactifications corresponding to enhanced gauge symmetry. We apply this to test the proposed F-theory/heterotic dualities in six dimensions. We recover the perturbative gauge symmetry enhancements of the heterotic side and the physics of small SO (32) instantons, and discover new mixed perturbative/nonperturbative gauge symmetry enhancements. Upon further toroidal compactification to four dimensions, we derive the chain of Calabi-Yau threefolds dual to various Coulomb branches of heterotic strings.

Orbifold resolution by D-branes

Abstract We study topological properties of the D-brane resolution of three-dimensional orbifold singularities, C 3 /Λ , for finite abelian groups Λ. The D-brane vacuum moduli space is shown to fill out the backgroun space-time with Fayet-Iliopoulos parameters controlling the size of the blow-ups. This D-brane vacuum moduli space can be classically described by a gauged linear sigma model, which is shown to be non-generic in a manner that projects out non-geometric regions in its phase diagram, as anticipated from a number of perspectives.

Mirror Symmetry for Two Parameter Models - II *

We describe in detail the space of the two Kahler parameters of the Calabi-Yau manifold P4(1,1,1,6,9)[18] by exploiting mirror symmetry. The large complex structure limit of the mirror, which corresponds to the classical large radius limit, is found by studying the monodromy of the periods about the discriminant locus, the boundary of the moduli space corresponding to singular Calabi-Yau manifolds. A symplectic basis of periods is found and the action of the Sp(6, Z) generators of the modular group is determined. From the mirror map we compute the instanton expansion of the Yukawa couplings and thes genralized N = 2 index, arriving at them numbers of instantons of genus zero and genus one of each bidegree. We find that these numbers can be negative, even in genus zero. We also investigate an SL(2, Z) symmetry that acts on a boundary of the moduli space.

FIVE-DIMENSIONAL SUPERSYMMETRIC GAUGE THEORIES AND DEGENERATIONS OF CALABI-YAU SPACES

Abstract We discuss five-dimensional supersymmetric gauge theories. An anomaly renders some theories inconsistent and others consistent only upon including a Wess-Zumino type Chern-Simons term. We discuss some necessary conditions for existence of non-trivial renormalization group fixed points and find all possible gauge groups and matter content which satisfy them. In some cases, the existence of these fixed points can be inferred from string duality considerations. In other cases, they arise from M-theory on Calabi-Yau threefolds. We explore connections between aspects of the gauge theory and Calabi-Yau geometry. A consequence of our classification of field theories with non-trivial fixed points is a fairly complete classification of a class of singularities of Calabi-Yau threefolds which generalize the “del Pezzo contractions” and occur at higher codimension walls of the Kahler cone.

Black hole condensation and the unification of string vacua

Abstract It is argued that black hole condensation can occur at conifold singularities in the moduli space of type II Calabi-Yau string vacua. The condensate signals a smooth transition to a new Calabi-Yau space with different Euler characteristic and Hodge numbers. In this manner string theory unifies the moduli spaces of many or possibly all Calabi-Yau vacua. Elementary string states and black holes are smoothly interchanged under the transitions, and therefore cannot be invariantly distinguished. Furthermore, the transitions establish the existence of mirror symmetry for many many or possibly all Calabi-Yau manifolds.

Calabi-Yau moduli space, mirror manifolds and spacetime topology change in string theory☆

A permanent magnet motor is provided which has first and second U-shaped sections comprising the motor stator. Each section is constructed of low reluctance magnetic material. The motor armature shaft passes through a hole in the bight of each section and carries a commutator. An air space separates the bight and shaft to provide a high reluctance path to the shaft. The two parallel sides of the first section fit between the two sides of the second section in a contact relation; the combination defining a two piece magnetic circuit that passes around the motor from end to end. The first section contains a permanent magnet mounted upon each of the sides at diametrically opposite locations adjacent the armature. The flux coupling the two magnets passes through the armature core. The magnets define a pole pair and are spaced very close to the edge of the armature core to minimize the air gap between the armature and the magnet. The first section is unbroken and provides a homogeneous flux path between the magnets. The second section provides a parallel-secondary flux path from the magnets. Additional low reluctance material is included on the bight of each section to compensate for the increased reluctance resulting from the hole through which the armature passes. Positioning stops are provided on the second section, which contact the first section as it is positioned, to establish the proper distal relation between the bights to accommodate the armature and commutator.

Summing the instantons: Quantum cohomology and mirror symmetry in toric varieties

Abstract We use the gauged linear sigma model introduced by Witten to calculate instanton expansions for correlation functions in topological sigma models with target space a toric variety V or a Calabi-Yau hypersurface M ⊂ V . In the linear model the instanton moduli spaces are relatively simple objects and the correlators are explicitly computable; moreover, the instantons can be summed, leading to explicit solutions for both kinds of models. In the case of smooth V , our results reproduce and clarify an algebraic solution of the V model due to Batyrev. In addition, we find an algebraic relation determining the solution for M in terms of that for V . Finally, we propose a modification of the linear model which computes instanton expansions about any limiting point in the moduli space. In the smooth case this leads to a (second) algebraic solution of the M model. We use this description to prove some conjectures about mirror symmetry, including the previously conjectured “monomial-divisor mirror map” of Aspinwall, Greene and Morrison.

Extremal transitions and five-dimensional supersymmetric field theories

We study five-dimensional supersymmetric field theories with one-dimensional Coulomb branch. We extend a previous analysis which led to non-trivial fixed points with En symmetry (E8, E7, E6, E5 = Spin(10), E4 = SU(5), E3 = SU(3) × SU(2), E2 = SU(2) × U(1) and E1 = SU(2)) by finding two new theories: E1 with U(1) symmetry and E0 with no symmetry. The latter is a non-trivial theory with no relevant operators preserving the super-Poincare symmetry. In terms of string theory these new field theories enable us to describe compactifications of the type I′ theory on S1Z2 with 16, 17 or 18 background D8-branes. These theories also play a crucial role in compactifications of M-theory on Calabi-Yau spaces, providing physical models for the contractions of del Pezzo surfaces to points (thereby completing the classification of singularities which can occur at codimension one in Kahler moduli). The structure of the Higgs branch yields a prediction which unifies the known mathematical facts about del Pezzo transitions in a quite remarkable way.