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

By Yosuke Imamura

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.Comment: 20 pages, LaTeX; v2: comments added; v3: minor corrections, version published in JHE

Topics: High Energy Physics - Theory
Year: 2011
DOI identifier: 10.1007/JHEP09(2011)133
OAI identifier: oai:arXiv.org:1104.4482
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