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 $n\geq3$, 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.
Primary authors
Ben Gripaios
(Cambridge)
Khoi Le Nguyen Nguyen
(University of Cambridge)
