BPS states in N=2 supersymmetric G2 and F4 models

In BPS quiver theory of N=2 supersymmetric pure gauge models with gauge invariance G, primitive BPS quivers Q0G are of two types: Q0ADE and Q0BCFG. In this study, we first show that Q0ADE have outer-automorphism symmetries inherited from the outer-automorphisms of the Dynkin diagrams of ADE Lie algebras. Then, we extend the usual folding operation of Dynkin diagrams ADE→BCFG to obtain the two following things: (i) relate Q0BCFG quivers and their mutations to the Q0ADE ones and their mutations; and (ii) link the BPS chambers of the N=2 ADE theories with the corresponding BCFG ones. As an illustration of this construction, we derive the BPS and anti-BPS states of the strong chambers QstgG2 and QstgF4 of the 4d N=2 pure G2 and F4 gauge models.