Classification of compactified $su(N_c)$ gauge theories with fermions in all representations

Understand

We classify $su(N_c)$ gauge theories on $\mathbb R^3\times \mathbb S^1$ with massless fermions in higher representations obeying periodic boundary conditions along $\mathbb S^1$.

• In particular, we single out the class of theories that is asymptotically free and weakly coupled in the infrared, and therefore, is amenable to semi-classical treatment.
• Our study is conducted by carefully identifying the vacua inside the affine Weyl chamber using Verma bases and Frobenius formula techniques.
• Theories with fermions in pure representations are generally strongly coupled.