Heterotic string compactification and quiver gauge theory on toric geometry

Thesis

This thesis is composed of papers in two areas: heterotic string model building on Calabi-Yau manifolds, and bipartite field theory with applications to brane tilings. However, the two streams share a common topic - string model building on toric geometry. Toric variety appears as both the ambient space for constructing Calabi- Yau hyper-surface, and the moduli space of D-brane configurations.

We study heterotic model building on 16 specific Calabi-Yau (CY) manifolds as hypersurfaces in toric four-folds. These 16 manifolds are the only ones among the more than half a billion manifolds in the Kreuzer-Skarke (KS) list with a non-trivial fundamental group. We classify the line bundle models on these manifolds, both for SU(5) and SO(10) Grand Unified Theories (GUT), which lead to consistent supersymmetric string vacua and they have three chiral families. In order to apply the model building to the whole KS list, we then systematically classify the freely-acting symmetries. For this purpose we develop a method of classifying all freely acting discrete groups of CY on toric spaces, and generate its weighted projective representations. A few new discrete symmetries are found and presented. This is the first step towards heterotic string model building on CYs constructed by re exive polytopes of KS list.

The second part of this thesis emphasises the applications of quiver gauge theory and dimer models. We generalise the results for quiver theories with low block numbers, revealing an new intriguing algebraic structure underlying a class of possible superconformal fixed points. After explicitly computing the Diophantine equation of five block cases, we use this structure to re-organize the result in a form that can be applied to arbitrary block numbers. We argue that these theories can be thought of as vectors in the root system of the corresponding quiver. In addition to exploring the block quiver theory, we also compute the large area toric models and their associated dimer models. We compute the Kasteleyn matrix of the conifolds and its orbifolds, then turn on the vacuum expectation value (vev.) for massless fields. New dimer models with large triangulation areas are classified and presented.

Authors: Sun, C

• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford