Week 22.03.2015 – 28.03.2015

It has been conjectured that the fundamental theory of strings and branes has an $E_{11}$ symmetry. I will explain how this conjecture leads to a generalized space-time, which is automatically equipped with its own geometry, as well as equations of motion for the fields that live on this generalized space-time.

Higher Gauge Theory is a categorical way of thinking about parallel transport of extended objects. Such parallel transport appears naturally within string and M-theory. In particular, the six-dimensional maximally superconformal theory or at least self-dual strings in four dimensions should be captured by Higher Gauge Theory. I will review some of my recent work in this area, including how M2-brane models fit into the picture, how twistor geometry can yield field equations containing the non-abelian tensor multiplet and give explicit higher versions of the BPST instanton and the 't Hooft-Polyakov monopole. If time permits, I will also talk a bit about a higher version of the IKKT matrix model.