Looking for the $G_2$ Higgs Branch of 4D Rank 1 SCFTs
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866910535234093056 |
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| author | Abhishek, Md. Grover, Sachin Jatkar, Dileep P. Singh, Kajal |
| author_facet | Abhishek, Md. Grover, Sachin Jatkar, Dileep P. Singh, Kajal |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_00275 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Looking for the $G_2$ Higgs Branch of 4D Rank 1 SCFTs Abhishek, Md. Grover, Sachin Jatkar, Dileep P. Singh, Kajal High Energy Physics - Theory 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. |
| title | Looking for the $G_2$ Higgs Branch of 4D Rank 1 SCFTs |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2312.00275 |