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arXiv · 1104.4482

Relation between the 4d superconformal index and the S^3 partition function

Yosuke Imamura
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Abstract

A relation between the 4d superconformal index and the S^3 partition function is studied with focus on the 4d and 3d actions used in localization. In the case of vanishing Chern-Simons levels and round S^3 we explicitly show that the 3d action is obtained from the 4d action by dimensional reduction up to terms which do not affect the exact results. By combining this fact and a recent proposal concerning a squashing of S^3 and SU(2) Wilson line, we obtain a formula which gives the partition function depending on the Weyl weight of chiral multiplets, real mass parameters, FI parameters, and a squashing parameter as a limit of the index of a parent 4d theory.

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Yosuke Imamura. 2011-10-12. Relation between the 4d superconformal index and the S^3 partition function. https://doi.org/10.1007/jhep09(2011)133

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