This series consists of talks in the area of Superstring Theory.
In string compactifications, Kahler metrics for chiral matter fields are an essential prerequisite for the computation of soft supersymmetry breaking terms. I describe new techniques for computing these in Calabi-Yau string compactifications. This involves deducing the modular behaviour of the Kahler metric from that of the physical Yukawa couplings. Using these techniques I derive Kahler metrics for both KKLT and large-volume models. For the latter case, I discuss two applications.
TBA
Studies of ${cal N}=4$ super Yang Mills operators with large R-charge have shown that, in the planar limit, the problem of computing their dimensions can be viewed as a certain spin chain. These spin chains have fundamental ``magnon\'\' excitations which obey a dispersion relation that is periodic in the momentum of the magnons. This result for the dispersion relation was also shown to hold at arbitrary \'t Hooft coupling. Here we identify these magnons on the string theory side and we show how to reconcile a periodic dispersion relation with the continuum worldsheet description.
Geometric flows, especially the Ricci flow, have been used with considerable success in recent years to address the Poincare and Thurston conjectures for 3-manifolds. In this talk, I will briefly introduce these geometric flows, and describe how they appear in a completely different context in the physics of string theory. I will then outline how recently developed techniques in geometric flows could be used to address questions of importance in string theory.