论文标题
$ s^1 $减少4D $ \ MATHCAL {N} = 3 $ scfts和ABJM理论的独立性
$S^1$ Reduction of 4D $\mathcal{N}=3$ SCFTs and Squashing Independence of ABJM Theories
论文作者
论文摘要
我们研究了4D $ \ MATHCAL {N} = 3 $ SUPERCORN -CORTINGAL FIELD THERIONS（SCFTS）的紧凑型，重点介绍了4D超符号索引与Squashed Spheed Sphere $ S^3_b $上的4D SuperConformal Index和3D分区功能之间的关系。由于中心$ \ mathfrak {u}（1）$的$ \ mathfrak {u}（3）4D理论的$ r-对称性可以与$ \ mathcal {n} = 6 $ abelian风味对称性在三个维度上，因此，对于全局的4D/3D而言，对于全球对中的精确介绍了。专注于3D理论是ABJM理论的情况，我们证明了上述R-对称混合可以通过考虑4D索引的Schur极限（和/或其$ \ Mathcal {n} = 3 $ COUSIN）来精确识别。结果，我们概括了ABJM理论的最新讨论，讨论了4D索引的超对称性增强与压制$ S^3_b $分区功能的独立性之间的联系。
We study the compactification of 4D $\mathcal{N}=3$ superconformal field theories (SCFTs) on $S^1$, focusing on the relation between the 4D superconformal index and 3D partition function on the squashed sphere $S^3_b$. Since the center $\mathfrak{u}(1)$ of the $\mathfrak{u}(3)$ R-symmetry of the 4D theory can mix with an $\mathcal{N}=6$ abelian flavor symmetry in three dimensions, the precise 4D/3D relation for the global symmetry is not obvious. Focusing on the case in which the 3D theory is the ABJM theory, we demonstrate that the above R-symmetry mixing can be precisely identified by considering the Schur limit (and/or its $\mathcal{N}=3$ cousin) of the 4D index. As a result, we generalize to the ABJM theories recent discussions on the connection between supersymmetry enhancement of the 4D index and squashing independence of the $S^3_b$ partition function.
