Timo Weigand (Heidelberg)
U(1) gauge symmetries are ubiquitous in string compactifications. They are well known to play an important role in model building as selection rules in the effective action. As such they have also been heavily invoked in recent approaches to F-theory model building. However, in this framework the geometric origin of abelian gauge fields is relatively poorly understood. Thus the quest for U(1) symmetries in F-theory is a topic both of phenomenological relevance and of interest in its own right.
We will discuss the appearance of U(1) symmetries in F-theory from a geometric and field theoretic perspective and compare the situation to the well understood case of perturbative Type IIB orientifolds. We will discuss two different mechanisms that can make a perturbatively present U(1) symmetry disappear in F-theory: A geometric Stuckelberg mechanism and Higgsing. Both have very different geometric origins and also bear different consequences for the phenomenology of the 4-dimensional field theory. As an application we will identify the restrictions on the elliptic fibration that guarantee a U(1) symmetry in F-theory compactifications with a Grand Unified SU(5) gauge symmetry. If time permits we will also comment on the role of M5/D3-instantons and implications for moduli stabilisation.
Arnold Sommerfeld Center