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arXiv · 1401.7952

Superfield theories on $S^3$ and their localization

I. B. Samsonov·D. Sorokin
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Abstract

We consider the superfield formulation of supersymmetric gauge and matter field theories on a three-dimensional sphere with rigid ${\cal N}=2$ supersymmetry, as well as with ${\cal N}> 2$. 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.

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I. B. Samsonov, D. Sorokin. 2014-02-25. Superfield theories on $S^3$ and their localization. https://doi.org/10.1007/jhep04(2014)102

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