On N = 1 gauge models from geometric engineering in M-theory

We study geometric engineering of four-dimensional N = 1 gauge models from M-theory on a seven-dimensional manifold with G2 holonomy. The manifold is constructed as a K3 fibration over a three-dimensional base space with ADE geometry. The resulting gauge theory is discussed in the realm of (p, q) webs. We discuss how the anomaly cancellation condition translates into a condition on the associated affine ADE Lie algebras.