Abstract

F-theory is a strong coupling formulation of Type IIB string theory which unifies gravitational and gauge theory data of 7-branes in the geometry of elliptic fibrations. In all situations of interest such fibrations are singular spaces, and, in order to describe the low-energy physics, one typically removes the singularities either via resolutions or deformations. In this talk, I will propose a framework which instead allows us to deal with the singular spaces directly. I will show how, besides correctly reproducing known results, this treatment enables us to explore branches of the string moduli space which are invisible to the smooth phase. The method is based on the so called “matrix factorizations of hypersurface singularities”, and I will discuss it at work in a number of examples, including a class of globally defined, four-dimensional models. The talk is based on arXiv:1410.4178 and arXiv:1410.4867.