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arXiv · 2312.00275

Looking for the $G_2$ Higgs Branch of 4D Rank 1 SCFTs

Md. Abhishek·Sachin Grover·Dileep P. Jatkar·Kajal Singh
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Abstract

The Schur index of the Higgs branch of 4-dimensional $\mathcal{N}=2$ 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 $(A_0, A_{\frac{1}{2}}, A_1, A_2, D_4)$ 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.

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Md. Abhishek, Sachin Grover, Dileep P. Jatkar, Kajal Singh. 2023-12-01. Looking for the $G_2$ Higgs Branch of 4D Rank 1 SCFTs. https://arxiv.org/abs/2312.00275

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