Notes on SUSY gauge theories on three-sphere

By Naofumi Hama, K. Hosomichi, Sungjay Lee. 2010

576 citations recorded by the source corpus.

We extend theformulaforpartitionfunctions of $$\mathcal{N}=2 $$ superconformalgauge theories on S3 obtained recently by Kapustin, Willett and Yaakov, to incorporate matter fields with arbitrary R-charge assignments. We use the result to check that the self-mirror property of $$\mathcal{N}=4 $$ SQED with two electron hypermultiplets is preserved under a certain mass deformation which breaks the supersymmetry to $$\mathcal{N}=2 $$.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/7151186daf9173cb14460473550aca7493957625

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In Atomic and Molecular Physics, and Optics

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Citations in the corpus

The perturbative partition function of supersymmetric 5D Yang-Mills theory with matter on the five-sphere (2012, background): “For the matrix models arising from localization of 3D gauge theories [8, 10, 11, 12, 13] the famous N dependence of the free energy has been successfully demonstrated in different models, see for example [22, 23, 24, 25, 26, 27, 13].”
Exact Kähler potential from gauge theory and mirror symmetry (2012, background): “In [16] the authors have pointed out that superconformality and unitarity are not respected in the framework of the exact three-sphere partition function [17, 18, 19] due to unitarity violating terms inevitable when putting rigid supersymmetric theories on a curved manifold, even though the theories”
Contact terms, unitarity, and F -maximization in three-dimensional superconformal theories (2012, methodology): “Here we are interested in round spheres [23-25,27].”
Defects and quantum Seiberg-Witten geometry (2014, methodology): “1 S3 Partition function Let us begin by summarizing the supersymmetric partition function of 3d N = 4 gauge theories on squashed S3, as computed using supersymmetric localization in [9, 10, 32].”
Exploring curved superspace (2012, background): “Following [7-10], much work has focused on supersymmetric theories on round spheres.”
Comments on 3d Seiberg-like dualities (2011, methodology): “More generally, mixing a global symmetry U(1)I with the R-symmetry corresponds to giving an imaginary part to the real mass mI according to [54, 55, 21] mI → mI + ω aI ⇔ R → R + aIQI , (5.”
Index for three dimensional superconformal field theories with general R-charge assignments (2011, methodology): “By using these action, we can compute the exact partition function in S(3)[5, 6, 7].”
Correlation functions of Coulomb branch operators (2016, unknown): “For some previous work on the partition function of SCFTs on spheres consult [1–3,19–22].”
Interpolating between a and F (2014, background): “Indeed, the supersymmetric Lagrangian for a free chiral multiplet with non-canonical dimension ∆ is given by [18, 19, 91]”
Towards the F-theorem: $ \mathcal{N} = 2 $ field theories on the three-sphere (2011, methodology): “The localization of the free energy for such theories, which allows for varying the R-charges of the fields, was carried out in [11,20], and we used their results to write down and solve a variety of large N matrix models with the method introduced in [10].”
A universal counting of black hole microstates in AdS4 (2017, background): “Recall that the free energy FS3 is a function of a set of trial R-charges that parameterize a family of supersymmetric Lagrangians on S(3) [28, 34].”
The exact superconformal R-symmetry extremizes Z (2010, result): “See also [37] that appeared shortly after the first version of this paper, which derived the same result also using localization of non-conformal R-symmetric N = 2 theories on S(3).”
ABJM theory as a Fermi gas (2011, background): “theories with N ≥ 2 supersymmetry in [3, 4].”
4d Index to 3d Index and 2d TQFT (2011, background): “Recent studies have uncovered powerful techniques (mostly based on localization) to extract exact results for 3d and 4d supersymmetric gauge theories, including the 4d N ≥ 1 superconformal index on S(1) × S(3) [1, 2], the 4d N ≥ 2 partition function on S(4) [3], the 3d N ≥ 2 partition function on S(”
SUSY gauge theories on squashed three-spheres (2011, methodology): “[4]) except that the radius of round S3 is replaced by l̃.”
Instanton bound states in ABJM theory (2013, methodology): “It was shown in [2, 3, 4] that the partition function and vacuum expectation values of BPS Wilson loops in 3d supersymmetric Chern-Simons theories including the ABJM theory are reduced to finite-dimensional matrix integrals after the localization technique [5] is applied.”