Squashing and supersymmetry enhancement in three dimensions

Abstract

We consider mass-deformed theories with $\mathcal{N}\ge 2$ supersymmetry on round and squashed three-spheres. By embedding the supersymmetric backgrounds in extended supergravity we show that at special values of mass deformations the supersymmetry is enhanced on the squashed spheres. When the $3d$ partition function can be obtained by a limit of a $4d$ index we also show that for these special mass deformations only the states annihilated by extra supercharges contribute to the index. By using an equivalence between partition functions on squashed spheres and ellipsoids, we explain the recently observed squashing independence of the partition function of mass-deformed ABJ(M) theory on the ellipsoid. We provide further examples of such simplification for various $3d$ supersymmetric theories.

arXiv comment15+9 pages

References in corpus (31)

• Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
• Rigid Supersymmetric Theories in Curved Superspace
• SUSY Gauge Theories on Squashed Three-Spheres
• Gauge Theories and Macdonald Polynomials
• Localization techniques in quantum field theories
• 3d dualities from 4d dualities
• Supersymmetric Field Theories on Three-Manifolds
• The Geometry of Supersymmetric Partition Functions
• N=2 supersymmetric theories on squashed three-sphere
• $\mathcal{N}=4$ Super-Yang-Mills Correlators at Strong Coupling from String Theory and Localization
• 4d Index to 3d Index and 2d TQFT
• From 4d superconformal indices to 3d partition functions
• Seiberg-Witten Theories on Ellipsoids
• Far Beyond the Planar Limit in Strongly-Coupled $\mathcal{N}=4$ SYM
• Perturbative partition function for a squashed S^5
• Modular Invariance in Superstring Theory From $\mathcal{N}=4$ Super-Yang-Mills
• New Modular Invariants in $\mathcal{N}=4$ Super-Yang-Mills Theory
• The M-Theory S-Matrix From ABJM: Beyond 11D Supergravity
• Three-sphere free energy for classical gauge groups
• Extended Supersymmetry on Curved Spaces
• Reducing the 4d Index to the S^3 Partition Function
• Localization on three-dimensional manifolds
• 3d $\mathcal{N}=4$ OPE Coefficients from Fermi Gas
• Twisting with a Flip (the Art of Pestunization)
• Squashing, Mass, and Holography for 3d Sphere Free Energy
• N=6 conformal supergravity in three dimensions
• Exact results in N=2 gauge theories
• Partition Function of $N=2$ Gauge Theories on a Squashed $S^4$ with $SU(2)\times U(1)$ Isometry
• Conformal field theories on deformed spheres, anomalies, and supersymmetry
• $\mathcal{N}=2$ Supergravity in $D=4,5,6$ Dimensions
• Flavor deformations and supersymmetry enhancement in $4d$ $\mathcal{N}=2$ theories

Cited by in corpus (6)

• Large $N$ Partition Functions of the ABJM Theory
• One-Dimensional Sectors From the Squashed Three-Sphere
• Dualities and loops on squashed $S^3$
• $S^1$ Reduction of 4D $\mathcal{N}=3$ SCFTs and Squashing Independence of ABJM Theories
• Flavor deformations and supersymmetry enhancement in $4d$ $\mathcal{N}=2$ theories
• The Holographic Contributions to the Sphere Free Energy