Effective actions from string and M-theory

Abstract

In this thesis we study the emergence of four-dimensional effective actions from compactifications of higher-dimensional string/M-theory and explore some of their phenomenological implications.<br /> In order to compactify eleven-dimensional M-theory to a four-dimensional effective <em>N</em>=1 supergravity action, the relevant internal spaces turn out to be <em>G₂</em>-manifolds. Contrary to Calabi-Yau manifolds appearing in compactifications of string theory, the construction of <em>G₂</em>-manifolds is not directly obtained via standard techniques of complex algebraic geometry. For this reason, there were up to now only a few hundred examples of them. In the first part of this thesis, we find many novel examples of <em>G₂</em>-manifolds based on the so-called twisted connected sum construction. Furthermore, we identify a limit in which the <em>G₂</em>-metric is approximated in terms of the metrics of the constituents of this constructions, allowing for the identification of universal moduli fields in the four-dimensional effective spectrum. A final expression for a (positive-definite) Kaehler potential in terms of these moduli is obtained, together with interesting Abelian and non-Abelian enhanced supersymmetric (<em>N</em>=2 and<em> N</em>=4) gauge theory sectors including, for example, the Standard Model gauge group and possible grand unification scenarios.<br /> In the second part we investigate the emergence of dark matter candidates from effective actions. Here we already start with a four-dimensional effective action motivated from F-theory/type IIB string theory on Calabi-Yau manifolds in the Kallosh-Linde (KL) moduli stabilization scenario. The non-positive vacuum in the KL scenario is uplifted by the Intriligator-Seiberg-Shih (ISS) sector, based on the free magnetic dual of <em>N</em>=1 supersymmetric QCD. We analyze interactions between the KL-ISS and the Minimal Supersymmetric Standard Model (MSSM) sectors in order to investigate the dynamics after the inflationary phase, obtaining constraints from late entropy production. Finally, we obtain neutralino dark matter candidates compatible with the observed dark matter relic density from both thermal and non-thermal production.