Cooking pasta with Lie groups

We extend the (gauged) Skyrme model to case in which global isospin group (which usually is taken be $SU(N)$) a generic compact connected Lie $G$. analyze corresponding field equations (3+1) dimensions from theory point of view. Several solutions can constructed analytically and are determined by embeddings three dimensional simple groups into $G$, irreducible representation. These represent so-called nuclear pasta state configurations matter at low energy. employ Dynkin explicit classification all subgroups exceptional classify such $G$ an group, give ingredients construct them explicitly. As example, we for $G=G_{2}$. then our ansatz include minimal coupling $U(1)$ gauge field. definition topological charge this concentrate attention electromagnetic case. After imposing "free force condition" on field, complete set coupled gauged minimally Abelian reduced just one linear ODE keeping alive charge. discuss cases belongs (Whittaker-)Hill Mathieu types.