The BPS spectrum of the 4d N=2 SCFT's H_1, H_2, D_4, E_6, E_7, E_8

TL;DR

This work systematically constructs canonical finite BPS chambers for all rank-1 ${\cal N}=2$ SCFTs in the $H_1,H_2,D_4,E_6,E_7,E_8$ sequence by employing BPS quivers $Q(r,s)$ and the mutation algorithm. The authors show that each theory admits a finite chamber containing exactly $n_h=2h(F)$ hypermultiplets, with $n_h=12(\Delta-1)$, and that the spectrum saturates the central charge $c$, revealing striking numerology and consistency with 2d/4d correspondences. They provide explicit constructions: for $H_1,H_2,D_4,E_6$ via Dynkin-subbquiver decompositions yielding $4,6,12,24$ hypers; for $E_7$ and $E_8$ through concrete mutation sequences producing 36 and 60 hypers, respectively, with detailed charge content and unbroken flavor symmetries. The decoupling analysis connects these finite chambers across the family through wall-crossing relations, offering nontrivial consistency checks and extending the known $D_2(G)$ and $D_p(SU(2))$ families. Overall, the results support a broader numerology conjecture and illuminate the BPS landscape of these interacting SCFTs.

Abstract

Extending results of arXiv:1112.3984, we show that all rank 1 N=2 SCFT's in the sequence H_1, H_2, D_4 E_6, E_7, E_8 have canonical finite BPS chambers containing precisely 2 h(F)=12(Delta-1) hypermultiplets. The BPS spectrum of the canonical BPS chambers saturates the conformal central charge c, and satisfies some intriguing numerology.