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

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 $S_b^3$. 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 $S_b^3$ partition function.

arXiv comment24 pages; 2nd version, minor changes made

References in corpus (36)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter
• Fractional M2-branes
• Infinite Chiral Symmetry in Four Dimensions
• Rigid Supersymmetric Theories in Curved Superspace
• SUSY Gauge Theories on Squashed Three-Spheres
• Notes on SUSY Gauge Theories on Three-Sphere
• Gauge Theories and Macdonald Polynomials
• N=5,6 Superconformal Chern-Simons Theories and M2-branes on Orbifolds
• On Short and Semi-Short Representations for Four Dimensional Superconformal Symmetry
• 3d dualities from 4d dualities
• The 4d Superconformal Index from q-deformed 2d Yang-Mills
• Cardy Formulae for SUSY Theories in d=4 and d=6
• From 4d superconformal indices to 3d partition functions
• N=3 four dimensional field theories
• On the Superconformal Index of Argyres-Douglas Theories
• S-folds and 4d N=3 superconformal field theories
• Relation between the 4d superconformal index and the S^3 partition function
• VOAs labelled by complex reflection groups and 4d SCFTs
• High-temperature asymptotics of supersymmetric partition functions
• On 4d rank-one N=3 superconformal field theories
• Reducing the 4d Index to the S^3 Partition Function
• Constraints on Chiral Operators in N=2 SCFTs
• Argyres-Douglas Theories, S^1 Reductions, and Topological Symmetries
• Elliptic hypergeometric integrals and 't Hooft anomaly matching conditions
• High-Temperature Expansion of Supersymmetric Partition Functions
• The superconformal index and an elliptic algebra of surface defects
• Finite $N$ Corrections to the Superconformal Index of S-fold Theories
• Squashing, Mass, and Holography for 3d Sphere Free Energy
• Exceptional $\mathcal{N}=3$ theories
• $c-a$ from the $N=1$ superconformal index
• An N=1 Lagrangian for an N=3 SCFT
• Minimal Distances Between SCFTs
• Squashing and supersymmetry enhancement in three dimensions
• Superconformal index of N=3 orientifold theories
• Macdonald Indices for Four-dimensional $\mathcal{N}=3$ Theories

Cited by in corpus (1)

• Dualities and loops on squashed $S^3$