Katrin Becker

Compactifications of heterotic theory on non-Kähler complex manifolds, I

We study new compactifications of the SO(32) heterotic string theory on compact complex non-K?hler manifolds. These manifolds have many interesting features like fewer moduli, torsional constraints, vanishing Euler character and vanishing first Chern class, which make the four-dimensional theory phenomenologically attractive. We take a particular compact example studied earlier and determine various geometrical properties of it. In particular we calculate the warp factor and study the sigma model description of strings propagating on these backgrounds. The anomaly cancellation condition and enhanced gauge symmetry are shown to arise naturally in this framework, if one considers the effect of singularities carefully. We then give a detailed mathematical analysis of these manifolds and construct a large class of them. The existence of a holomorphic (3,0) form is important for the construction. We clarify some of the topological properties of these manifolds and evaluate the Betti numbers. We also determine the superpotential and argue that the radial modulus of these manifolds can actually be stabilized.

Compactifications of heterotic strings on non-Kähler complex manifolds II

Abstract We continue our study of heterotic compactifications on non-Kahler complex manifolds with torsion. We give further evidence of the consistency of the six-dimensional manifold presented earlier and discuss the anomaly cancellation and possible supergravity description for a generic non-Kahler complex manifold using the newly proposed superpotential. The manifolds studied in our earlier papers had zero Euler characteristics. We construct new examples of non-Kahler complex manifolds with torsion in lower dimensions, that have nonzero Euler characteristics. Some of these examples are constructed from consistent backgrounds in F-theory and therefore are solutions to the string equations of motion. We discuss consistency conditions for compactifications of the heterotic string on smooth non-Kahler manifolds and illustrate how some results well known for Calabi–Yau compactifications, including counting the number of generations, apply to the non-Kahler case. We briefly address various issues regarding possible phenomenological applications.

Heterotic Strings with Torsion

In this paper we describe the heterotic dual of the type-IIB theory compactified to four dimensions on a toroidal orientifold in the presence of fluxes. The type-IIB background is most easily described in terms of an -theory compactification on a four-fold. The heterotic dual is obtained by performing a series of U-dualities. We argue that these dualities preserve supersymmetry and that the supergravity description is valid after performing them. The heterotic string is compactified on a manifold that is no longer Kahler and has torsion. These manifolds have to satisfy a number of constraints, for example, existence of an holomorphic three-form, size limits, torsional equations etc. We give an explicit form of the background and study the constraints associated to them.

M-theory inflation from multi M5-brane dynamics

Abstract We derive inflation from M-theory on S 1 / Z 2 via the non-perturbative dynamics of N M5-branes. The open membrane instanton interactions between the M5-branes give rise to exponential potentials which are too steep for inflation individually but lead to inflation when combined together. The resulting type of inflation, known as assisted inflation, facilitates considerably the requirement of having all moduli, except the inflaton, stabilized at the beginning of inflation. During inflation the distances between the M5-branes, which correspond to the inflatons, grow until they reach the size of the S 1 / Z 2 orbifold. At this stage the M5-branes will reheat the universe by dissolving into the boundaries through small instanton transitions. Further flux and non-perturbative contributions become important at this late stage, bringing inflation to an end and stabilizing the moduli. We find that with moderate values for N, one obtains both a sufficient amount of e-foldings and the right size for the spectral index.

In the realm of the geometric transitions

Abstract We complete the duality cycle by constructing the geometric transition duals in the type IIB, type I and heterotic theories. We show that in the type IIB theory the background on the closed string side is a Kahler deformed conifold, as expected, even though the mirror type IIA backgrounds are non-Kahler (both before and after the transition). On the other hand, the type I and heterotic backgrounds are non-Kahler. Therefore, on the heterotic side these backgrounds give rise to new torsional manifolds that have not been studied before. We show the consistency of these backgrounds by verifying the torsional equation.

String Theory and M-Theory: Frontmatter

1. Introduction 2. The bosonic string 3. Conformal field theory and string interactions 4. Strings with world-sheet supersymmetry 5. Strings with space-time supersymmetry 6. T-duality and D-branes 7. The heterotic string 8. M-theory and string duality 9. String geometry 10. Flux compactifications 11. Black holes in string theory 12. Gauge theory/string theory dualities References Index.

Geometric Transitions, Non-Kahler Geometries and String Vacua

We summarize an explicit construction of a duality cycle for geometric transitions in type II and heterotic theories. We emphasize that the manifolds with torsion constructed with this duality cycle are crucial for understanding different phenomena appearing in effective field theories.

PP-waves, M-theory and fluxes

We study a new type of warped compactifications of M-theory on eight-manifolds for which nowhere vanishing covariantly constant spinors of indefinite chirality on the internal manifold can be found. We derive the constraints on the fluxes and the warp factor following from supersymmetry and the equations of motion. We show, that the lift of type IIB pp-waves to M-theory is a special type of solution of this general class of models. We comment on the relation between the type IIB version of such compactifications as a dual description of the Polchinski–Strassler solution describing a four-dimensional confining gauge theory.

A note on fluxes in six-dimensional string theory backgrounds

Abstract We study the structure of warped compactifications of type IIB string theory to six space–time dimensions. We find that the most general four-manifold describing the internal dimensions is conformal to a Kahler manifold, in contrast with the heterotic case where the four-manifold must be conformally Calabi–Yau.

String Theory and M-Theory: The bosonic string

This chapter introduces the simplest string theory, called the bosonic string. Even though this theory is unrealistic and not suitable for phenomenology, it is the natural place to start. The reason is that the same structures and techniques, together with a number of additional ones, are required for the analysis of more realistic superstring theories. This chapter describes the free (noninteracting) theory both at the classical and quantum levels. The next chapter discusses various techniques for introducing and analyzing interactions. A string can be regarded as a special case of a p -brane, a p -dimensional extended object moving through space-time. In this notation a point particle corresponds to the p = 0 case, in other words to a zero-brane. Strings (whether fundamental or solitonic) correspond to the p = 1 case, so that they can also be called one-branes. Two-dimensional extended objects or two-branes are often called membranes. In fact, the name p -brane was chosen to suggest a generalization of a membrane. Even though strings share some properties with higher-dimensional extended objects at the classical level, they are very special in the sense that their two-dimensional world-volume quantum theories are renormalizable, something that is not the case for branes of higher dimension. This is a crucial property that makes it possible to base quantum theories on them. In this chapter we describe the string as a special case of p -branes and describe the properties that hold only for the special case p = 1.