$S^1$ reduction of 4D $\mathcal{N}=4$ Schur index and 3D $\mathcal{N}=8$ mass-deformed partition function
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| Format: | Preprint |
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2024
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| _version_ | 1866912171996217344 |
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| author | Nakanishi, Tomoki Nishinaka, Takahiro |
| author_facet | Nakanishi, Tomoki Nishinaka, Takahiro |
| contents | We study the compactification of 4D $\mathcal{N}=4$ SYM on $S^1$ from the viewpoint of the superconformal index. In the cases that the gauge group of the 4D SYM is $U(N)$ and $Usp(2N)$, the resulting 3D theory is believed to be the ABJM theory with the Chern-Simons level $k=1$ and $k=2$, respectively. This suggests that the small $S^1$ limit of the superconformal index of these 4D $\mathcal{N}=4$ SYMs is identical to the sphere partition function of the ABJM theories. Using a recently observed relation between the 4D and 3D R-charges for theories with twelve or more supercharges, we explicitly confirm this identity in the Schur limit of the 4D index. Our result provides a direct quantitative check of the relation between 4D $\mathcal{N}=4$ SYMs and 3D $\mathcal{N}=8$ ABJM theories. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_20452 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $S^1$ reduction of 4D $\mathcal{N}=4$ Schur index and 3D $\mathcal{N}=8$ mass-deformed partition function Nakanishi, Tomoki Nishinaka, Takahiro High Energy Physics - Theory We study the compactification of 4D $\mathcal{N}=4$ SYM on $S^1$ from the viewpoint of the superconformal index. In the cases that the gauge group of the 4D SYM is $U(N)$ and $Usp(2N)$, the resulting 3D theory is believed to be the ABJM theory with the Chern-Simons level $k=1$ and $k=2$, respectively. This suggests that the small $S^1$ limit of the superconformal index of these 4D $\mathcal{N}=4$ SYMs is identical to the sphere partition function of the ABJM theories. Using a recently observed relation between the 4D and 3D R-charges for theories with twelve or more supercharges, we explicitly confirm this identity in the Schur limit of the 4D index. Our result provides a direct quantitative check of the relation between 4D $\mathcal{N}=4$ SYMs and 3D $\mathcal{N}=8$ ABJM theories. |
| title | $S^1$ reduction of 4D $\mathcal{N}=4$ Schur index and 3D $\mathcal{N}=8$ mass-deformed partition function |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2412.20452 |