English

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

High Energy Physics - Theory 2015-05-27 v3

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.

Keywords

Cite

@article{arxiv.1104.4482,
  title  = {Relation between the 4d superconformal index and the S^3 partition function},
  author = {Yosuke Imamura},
  journal= {arXiv preprint arXiv:1104.4482},
  year   = {2015}
}

Comments

20 pages, LaTeX; v2: comments added; v3: minor corrections, version published in JHEP

R2 v1 2026-06-21T17:57:51.043Z