Melanie 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.

Supersymmetry breaking, M-theory and fluxes

We consider warped compactifications of Script M-theory to three-dimensional Minkowski space on compact eight-manifolds. Taking all the leading quantum gravity corrections of eleven-dimensional supergravity into account we obtain the solution to the equations of motion and Bianchi identities. Generically these vacua are not supersymmetric and yet have a vanishing three-dimensional cosmological constant.

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.

De Sitter vacua from heterotic M-theory

It is shown how metastable de Sitter vacua might arise from heterotic M-theory. The balancing of its two non-perturbative effects, open membrane instantons against gaugino condensation on the hidden boundary, which act with opposing forces on the interval length, is used to stabilize the orbifold modulus (dilaton) and other moduli. The non-perturbative effects break supersymmetry spontaneously through F-terms which leads to a positive vacuum energy density. In contrast to the situation for the weakly coupled heterotic string, the charged scalar matter fields receive non-vanishing vacuum expectation values and therefore masses in a phenomenologically relevant regime. It is important that in order to obtain these de Sitter vacua we are not relying on exotic effects or fine-tuning of parameters. Vacua with more realistic supersymmetry breaking scales and gravitino masses are obtained by breaking the hidden E8 gauge group down to groups of smaller rank. Also small values for the open membrane instanton Pfaffian are favored in this respect. Finally we outline how the incorporation of additional flux superpotentials can be used to stabilize the remaining moduli.

Geometric transitions, flops and non-Kähler manifolds: II

Abstract We continue our study of geometric transitions in type II and heterotic theories. In type IIB theory we discuss an F-theory setup which clarifies many of our earlier assumptions and allows us to study gravity duals of N = 1 gauge theories with arbitrary global symmetry group G . We also point out the subtle differences between global and local metrics, and show that in many cases the global descriptions are far more complicated than discussed earlier. We determine the full global description in type I/heterotic theory. In type IIA, our analysis gives rise to a local non-Kahler metric whose global description involves a particular orientifold action with gauge fluxes localised on branes. We are also able to identify the three form fields that allow for a smooth flop in the M-theory lift. We briefly discuss the issues of generalized complex structures in type IIB theory and possible half-twisted models in the heterotic duals of our type II models. In a companion paper we will present details on the topological aspects of these models.

Compactifying M-theory to four dimensions

We consider compactifications of M-theory to four-dimensional Minkowski space on seven-dimensional non-compact manifolds. These compactifications include a warp factor which is non constant due to the presence of sources coming from five-branes wrapping two-dimensional submanifolds of the internal seven-dimensional space. We derive the expression for the field strengths and consider an explicit example of this general class of solutions.

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.

A Note on flux induced superpotentials in string theory

Non-vanishing fluxes in -theory and string theory compactifications induce a superpotential in the lower dimensional theory. Gukov has conjectured the explicit form of this superpotential. We check this conjecture for the heterotic string compactified on a Calabi-Yau three-fold as well as for warped -theory compactifications on Spin(7) holonomy manifolds, by performing a Kaluza-Klein reduction.

M-theory on Spin(7) manifolds, fluxes and 3D, N=1 supergravity

We calculate the most general causal N=1 three-dimensional, gauge invariant action coupled to matter in superspace and derive its component form using ectoplasmic integration theory. One example of such an action can be obtained by compactifying M-theory on a Spin(7) holonomy manifold taking non-vanishing fluxes into account. We show that the resulting three-dimensional theory is in agreement with the more general construction. The scalar potential resulting from Kaluza–Klein compactification stabilizes all the moduli fields describing deformations of the metric except for the radial modulus. This potential can be written in terms of the superpotential previously discussed in the literature.