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

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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 the4d 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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Authors and Affiliations

  1. Department of Physics, Tokyo Institute of Technology, Tokyo, 152-8551, Japan

    Yosuke Imamura

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  1. Yosuke Imamura
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Correspondence to Yosuke Imamura.

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ArXiv ePrint: 1104.4482

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Imamura, Y. Relation between the 4d superconformal index and the S 3 partition function. J. High Energ. Phys. 2011, 133 (2011). https://doi.org/10.1007/JHEP09(2011)133

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  • DOI: https://doi.org/10.1007/JHEP09(2011)133

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