Superfield theories on $S^3$ and their localization

Abstract

We consider the superfield formulation of supersymmetric gauge and matter field theories on a three-dimensional sphere with rigid $\mathcal{N}=2$ supersymmetry, as well as with $\mathcal{N}>2$. The construction is based on a supercoset $SU(2|1)/U(1)$ containing $S^3$ as the bosonic subspace. We derive an explicit form of $SU(2|1)/U(1)$ supervielbein and covariant derivatives, and use them to construct classical superfield actions for gauge and matter supermultiplets in this superbackground. We then apply superfield methods for computing one-loop partition functions of these theories and demonstrate how the localization technique works directly in the superspace.

1+64 pages; v2: Section 4.2 and a reference are added

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Cited by in corpus (13)

• Superconformal mechanics in SU(2|1) superspace
• Higher Spins in Hyper-Superspace
• Supersymmetric dS/CFT
• SU(2|2) supersymmetric mechanics
• Gauged spinning models with deformed supersymmetry
• N=4 supersymmetric Yang-Mills theories in AdS_3
• SU(2|1) mechanics and harmonic superspace
• Superconformal index on ${\mathbb{RP}}^2\times {\mathbb{S}}^1$ and mirror symmetry
• Higher spin supermultiplets in three dimensions: (2,0) AdS supersymmetry
• Deformed supersymmetric quantum mechanics with spin variables
• Superconformal structures on the three-sphere
• Gauge and matter superfield theories on $S^2$
• Mirror Symmetry And Loop Operators