Brian R. Greene

Duality in Calabi-Yau moduli space

We describe a duality in the moduli space of string vacua which pairs topologically distinct Calabi-Yau manifolds and shows that the yield isomorphic conformal theories. At the level of the geometrical description, this duality interchanges the roles of Kahler and complex structure moduli and thus pairs manifolds whose Euler numbers differ by χ → − χ. Amongst the interesting implications of this duality is the conclusion that by using both manifolds of a “mirror pair” the 273 and 273 couplings can be computed exactly by lowest-order geometrical calculations.

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.

Stringy Cosmic Strings and Noncompact Calabi-Yau Manifolds

We describe string vacuum configurations for which the radii (moduli) of the internal compact space vary in four-dimensional space-time, focusing on configurations which have the interpretation of cosmic strings. We will show that some of them admit Ricci-flat Kahler metrics (i.e. they correspond to noncompact Calabi-Yau manifolds), thus providing new vacuum solutions to the full string theory. One novel feature of some of these solutions is that the internal space decompactifies near the core of the cosmic string, without producing any physical singularities.

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.

Calabi-Yau manifolds and renormalization group flows

Using ideas of renormalization group flows we show how to represent a large class of Calabi-Yau manifolds in terms of renormalization group fixed points of Landau-Ginzburg models. In particular we show why Gepners construction yields Calabi-Yau compactifications. More precisely, we show that all of his models correspond to strings propagating on algebraic varieties in weighted projective spaces.

A three-generation superstring model: (II). Symmetry breaking and the low-energy theory

Abstract We discuss low-energy phenomenology for a three-generation model, based upon compactification on a specific Calabi-Yau manifold, with an underlying E8 ⊗ E8 symmetry following from the heterotic superstring. It is shown how a combination of breaking by flux loops and Higgs scalar vevs can lead to just the standard model at low energy. The discrete symmetries following from the compactification manifold give rise to a matter parity in the low energy theory which forbids dimension four baryon and lepton number violation. They also ensure a light pair of Higgs bosons and constrain the form of the light fermion mass matrix. The Kobayashi-Maskawa mixing matrix and light fermion masses are determined, and a relation is obtained between the mixing angles. The only light states additional to those of the supersymmetric standard model are a charged lepton and three neutral leptons. Neutrinos are massive but their mass is expected to be very small (⩽ O(10− eV)).

Aspects of (2, 0) string compactifications

This paper is devoted to the study of compactifications of the heterotic string with (2, 0) world sheet supersymmetry. This leads to a theory with N = 1 supersymmetry in spacetime. It has been claimed on general grounds that (2, 0) compactifications should not be solutions to the string equations of motion when the effect of world sheet instantons is taken into account. We find that this is not necessarily correct. We formulate a precise condition for a (2, 0) compactification to be a solution and construct the first explicit example of a nontrivial (2, 0) compactification on a Calabi-Yau manifold. We discuss general techniques for analysing the structure of the four-dimensional effective theories that result from (2, 0) compactifications.

Inflation as a probe of short distance physics

We show that a string-inspired Planck scale modification of general relativity can have observable cosmological effects. Specifically, we present a complete analysis of the inflationary perturbation spectrum produced by a phenomenological Lagrangian that has a standard form on large scales but incorporates a string-inspired short distance cutoff, and find a deviation from the standard result. We use the de Sitter calculation as the basis of a qualitative analysis of other inflationary backgrounds, arguing that in these cases the cutoff could have a more pronounced effect, changing the shape of the spectrum. Moreover, the computational approach developed here can be used to provide unambiguous calculations of the perturbation spectrum in other heuristic models that modify trans-Planckian physics and thereby determine their impact on the inflationary perturbation spectrum. Finally, we argue that this model may provide an exception to constraints, recently proposed by Tanaka and Starobinsky, on the ability of Planck-scale physics to modify the cosmological spectrum.

Warped compactifications in M and F theory

Abstract We study M and F theory compactifications on Calabi–Yau four-folds in the presence of non-trivial background flux. The geometry is warped and belongs to the class of p -brane metrics. We solve for the explicit warp factor in the orbifold limit of these compactifications, compare our results to some of the more familiar recently studied warped scenarios, and discuss the effects on the low-energy theory. As the warp factor is generated solely by backreaction, we may use topological arguments to determine the massless spectrum. We perform the computation for the case where the four-fold equals K3×K3 .