Theory HEP Seminar

M-theory and knots: first steps towards gaining physical intuition on knot invariants

Veronica Errasti Diez

McGill

Knot theory is a branch of topology that has for decades attracted mathematicians and physicists alike. In this talk, I will start by briefly introducing knots and their classification problem. This will naturally lead to the concept of knot invariants. I will then mention the different approaches to the computation of knot invariants and immediately focus on the most recent (still in development) approach. Such approach consists on the study of the moduli space of certain four-dimensional PDEs. Specifically, I will construct two distinct but related M-theory models that, upon compactification, give rise to the aforementioned PDEs. In the process, I will discuss supersymmetry constraints, topological twist, surface operators and derive the self-linking number of arbitrary knots. The talk will be based on arXiv:1608.05128 and arXiv:1702.07366.