YTF 24

Varieties of four-dimensional gauge theories

19 Dec 2024, 11:00

30m

Ph30 (Centre for Particle Theory)

Mathematical Structures in Quantum Field Theory

Speaker

Khoi Le Nguyen Nguyen (University of Cambridge)

Description

Given a gauge Lie algebra, it is natural to seek representations for four-dimensional spacetime fermions that are anomaly-free and complex. Even for irreducible representations, where the problem reduces to studying ${\mathfrak{su}}_n$ for $n\ge 3$, solutions seem to be few and far between: a trial-and-error scan by Eichten, Kang and Koh found only three for ${\mathfrak{su}}_5$, for example. In this talk, I will explain how concepts and constructs in algebraic geometry show that there are in fact infinitely many such representations and yield them all. In particular, I will show that the problem is nearly identical to finding chiral solutions to the $U(1)$ anomaly cancellation equations for $n$ Weyl fermions in four spacetime dimensions.

Presentation materials

YTF_2024_Varieties_Presentation.pdf