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arXiv · 2211.07421

$S^1$ Reduction of 4D $\mathcal{N}=3$ SCFTs and Squashing Independence of ABJM Theories

Tomoki Nakanishi·Takahiro Nishinaka
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Abstract

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.

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Tomoki Nakanishi, Takahiro Nishinaka. 2022-11-14. $S^1$ Reduction of 4D $\mathcal{N}=3$ SCFTs and Squashing Independence of ABJM Theories. https://doi.org/10.1007/jhep03(2023)255

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