F-theory GUTs: Global Aspects and Phenomenology

摘要

F-theory provides an ideal framework for studying and realizing supersymmetric Grand Unified Theories (GUTs) within string theory. We review recent developments in this subject, giving an outline of how the GUT gauge groups, matter fields and Yukawa couplings are realized geometrically from F-theory compactifications on singular elliptic Calabi-Yau fourfolds. The main emphasis of this exposition will be on global aspects of these compactifications: we review how to resolve the singular Calabi-Yau, thereby giving a concrete picture of how the fiber structure changes in codimension 2 and 3, where matter and Yukawas are realized. Furthermore, a complete understanding of the resolved geometry allows the construction of consistently quantized G_4-flux, and we explain the connection to analogous constructions in local models. Finally, we discuss how simple anomaly considerations lead to generic constraints on the spectra of the theories that can arise in the framework of F-theory GUT realizations, and summarize their potential phenomenological implications. This is a contribution to the proceedings of the String Math 2011 conference, which was held at the University of Pennsylvania.