Looking for the G2 Higgs branch of 4D rank 1 SCFTs

A bstract The Schur index of the Higgs branch of 4-dimensional N N = 2 SCFTs is related to the spectrum of non-unitary 2-dimensional CFTs. The rank 1 case has been shown to lead to the non-unitary CFTs with Deligne-Cvitanovic (DC) exceptional sequence of Lie groups. We show that a subsequence ( A 0 , A1/2 A 1 2 , A 1 , A 2 , D 4 ) within the non-unitary sequence is related to a subsequence in the Mathur-Mukhi-Sen (MMS) sequence of unitary theories. We show that 2D non-unitary G 2 theory is related to unitary E 6 theory, and using this result along with the Galois conjugation, we propose that the G 2 Higgs branch is a sub-branch of the E 6 Higgs branch.