Fox and Hedgehog Seminar Series - 'Borel resummation in supersymmetric QFT'

QFT is a beautiful yet mysterious framework, in which it is unfortunately rather hard to obtain exact results. In talks by Anton and Matthew we have seen some of the exciting new tools to make new numerical predictions in strongly-interacting regimes. In particular, Anton introduced resummation techniques for divergent perturbation series and showed how efficient the Padé-Borel approximation is in extracting non-perturbative predictions out of these. In this talk I want to present some of the amazing geometry that lies behind these resummation techniques.

In particular, I will introduce a QFT setting in which the Borel resummation yields new exact results: this is the arena of four-dimensional QFT's which are invariant under an additional supersymmetry. The dynamics of such QFT's is much more restricted, and as a consequence there is an incredibly rich interaction with many advanced topics in mathematics. With a rather simple example, I hope to convey the beauty of the Borel techniques and their importance for obtaining exact results in (at least) supersymmetric quantum field theory.