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

A bstract The Schur index of the Higgs branch of 4-dimensional $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 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 , $$ {A}_{\frac{1}{2}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>A</mml:mi> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mml:msub> </mml:math> , 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.