SUSY gauge theories on squashed three-spheres

By Naofumi Hama, K. Hosomichi, Sungjay Lee. 2011

538 citations recorded by the source corpus.

We study Euclidean 3D $ \mathcal{N} = 2 $ supersymmetric gauge theories on squashed three-spheres preserving isometries SU(2) × U(1) or U(1) × U(1). We show that, when a suitable background U(1) gauge field is turned on, these squashed spheres support charged Killing spinors and therefore $ \mathcal{N} = 2 $ supersymmetric gauge theories. We present the Lagrangian and supersymmetry rules for general gauge theories. The partition functions are computed using localization principle, and are expressed as integrals over Coulomb branch. For the squashed sphere with U(1) × U(1) isometry, its measure and integrand are identified with the building blocks of structure constants in Liouville or Toda conformal field theories with b ≠ 1.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/17a2d6a01f8468bcd375ea0f7d9c079ab384eefc

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Citations in the corpus

N=2 supersymmetric theories on squashed three-sphere (2011, methodology): “If there exists an SU(2)L singlet supercharge, which is actually the case in the SU(2)L × U(1)r symmetric squashing in [23], the cancellation occurs between modes with the same SU(2)L quantum numbers: (j, j)B ↔ (j, j − 1/2)F , or (j, j)B ↔ (j, j + 1/2)F .”
Contact terms, unitarity, and F -maximization in three-dimensional superconformal theories (2012, background): “8 Recently, it was found that various squashed spheres also admit rigid supersymmetry [44-50].”
Relation between the 4d superconformal index and the S3 partition function (2011, methodology): “This is a different situation from [25].”
Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constant (2012, background): “(2)The localization of the ABJM theory and related theories on various manifolds such as S(3) [24], S(1)×S(2) [25] and squashed S(3) [26] has also been considered.”
Rigid supersymmetric theories in curved superspace (2011, background): “Even though we do not discuss it here in detail, it is clear that the same issue with lack of reflection positivity applies to non-conformal N = 2 theories on S(4) [1-3] and on S(3) [4-20].”
A topologically twisted index for three-dimensional supersymmetric theories (2015, methodology): “In the general case, we could use the cohomological argument of appendix A along the lines of [36].”
Lectures on localization and matrix models in supersymmetric Chern–Simons-matter theories (2011, methodology): “They have also been used to compute supersymmetric indices in S2 × S1 [65, 53, 69] and to study Chern–Simons–matter theories in other three-manifolds [49, 43, 59].”
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].”
N$$ \mathcal{N} $$ = 1 supersymmetric indices and the four-dimensional A-model (2017, background): “[24, 81, 82], most of the field modes on M4 are paired by supersymmetry and cancel out between bosons and fermions.”
5-dim superconformal index with enhanced En global symmetry (2012, background): “In this case the base manifold is deformed only by j2 and thus it becomes 4d manifold preserving SU(2)1 × U(1)2 whose local geometry at the equator is the squashed S(3) investigated in [49, 50].”
The geometry of supersymmetric partition functions (2013, background): “In special cases, they are equivalent to the ellipsoid squashings with U(1) × U(1) isometry studied in [43], which only give rise to real γ, and the squashings of [44, 45].”
Comments on 3d Seiberg-like dualities (2011, background): “It can be generalized to the partition function for a U(1) × U(1) isometrically squashed 3-sphere (or hyperellipsoid) S(3) b [21]: Z S3 b = ∞ ∏”
Exact Kähler potential from gauge theory and mirror symmetry (2012, methodology): “We however choose a rather short-cut discussed in [13], instead of considering the ghost fields and some modifications on supersymmetry by BRST transformtaion.”
4d Index to 3d Index and 2d TQFT (2011, unknown): “the result of [25]) with the squashing parameter b = √ 1+η 1−η .”