Description
In this talk, I will discuss the classification of exotic matter representations arising in toroidal heterotic orbifolds that cannot be obtained through geometric engineering. We show that every such representation admits an interpretation as an embedding into the adjoint representation of a simple Lie algebra. Motivated by this, we argue more generally that consistent matter in string theory should arise through the Higgsing of an adjoint representation. Finally, we will discuss the relation to F-theory, where these constructions can be understood in terms of complex structure deformations or non-geometric T-brane configurations.
