Elliptic Fibrations for F-Theory Geometric Engineering

Student thesis: Doctoral ThesisDoctor of Philosophy

Abstract

String phenomenology aims to explain the physics of the universe in the context of string theory, the leading candidate to unify gravitational and quantum physics. A main ingredient in constructing such models is compactifying the ten-dimensional theory on a six-dimensional manifold, so that one is left with the four non-compact dimensions modelling space-time. Performing this step allows one to reformulate many physical phenomena as properties of the geometry of the compactication manifold, and to nd generic constraints on physical models using methods from algebraic geometry. One such phenomenon
in nature are gauge theories, both abelian and non-abelian. In this thesis, we
undertake a systematic investigation of the interplay of the two in compactications of F-theory. In F-theory, the relevant compactication spaces are elliptically bered Calabi-Yau manifolds. They are particularly well-suited to the study of gauge symmetries in string phenomenology, since they both allow the existence of exceptional gauge symmetries such as E6 as well as the localization of gauge degrees of freedom on subloci of the compacti-cation manifold. Specically, non-abelian gauge theories are encoded as singularities of
the elliptic bration, and the rational sections of the bration specify the abelian part of the gauge group. Using tools from algebraic geometry, we study singularities of elliptic brations with a group of rational sections of rank 1, i.e. with a single abelian gauge factor.
In the rst part of the thesis, we rene the spectral cover formalism, which is a way
to study local properties of the subloci of the compactication manifold on which gauge degrees of freedom are localized in F-theory. We do so by introducing the spectral divisor. The spectral divisor allows one to construct gauge
uxes in F-theory in a purely local description. We exemplify this construction for an elliptic bration with associated gauge group E6.
In the second part of the thesis, we use Tate's algorithm to obtain a comprehensive classication of singular bers and an explicit list of possible realizations of F-theory compactications with both an abelian and non-abelian gauge symmetries. This list is complete for low-rank gauge symmetries, which are most relevant for building models of the universe, and thus allows to completely classify all F-theory models with a single abelian gauge factor. In particular, this list includes phenomenologically interesting brations not considered in the literature before.
Date of Award2014
Original languageEnglish
Awarding Institution
  • King's College London
SupervisorJohn Ellis (Supervisor) & Sakura Schafer-Nameki (Supervisor)

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