Mitchell Institute for Fundamental Physics & Astronomy
College Station, Texas 77843
In this talk I will explore the interior of the field spaces of four-dimensional effective theories of gravity. In the first part of the talk I will discuss the notion of a moduli-dependent species scale in N=2 theories serving as an effective UV cutoff in gravitational theories. I will show that the one loop topological free energy F1 can be used as a measure for this moduli-dependent species scale by relating F1 to a gravitational version of the a-function. This relation allows us for a definition of the center of the moduli space as the point where F1 is minimized. In the second part of the talk I will then focus on gravitational theories with N=1 arising in F-theory compactifications. Using the spectrum of light BPS strings in these theories I will argue for the presence of novel strong coupling singularities in the interior of their scalar field space and will discuss the physics associated to them.