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2013

Localization on Three-Manifolds

Alday, Luis F., Martelli, Dario, Richmond, Paul et al.

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We consider supersymmetric gauge theories on Riemannian three-manifolds with the topology of a three-sphere.

The three-manifold is always equipped with an almost contact structure and an associated Reeb vector field.
We show that the partition function depends only on this vector field, giving an explicit expression in terms of the double sine function.
In the large N limit our formula agrees with a recently discovered two-parameter family of dual supergravity solutions.

Localization on Three-Manifolds · Around

Built on

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N. Hama, K. Hosomichi and S. Lee, “Notes on SUSY Gauge Theories on Three-Sphere,” JHEP 1103
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N. Hama, K. Hosomichi and S. Lee, “SUSY Gauge Theories on Squashed Three-Spheres,” JHEP 1105
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G. Festuccia and N. Seiberg, “Rigid Supersymmetric Theories in Curved Superspace,” JHEP 1106
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Original

2012

Cited alongside, same era.

D. Martelli, A. Passias and J. Sparks, “The gravity dual of supersymmetric gauge theories on a squashed three-sphere,” Nucl. Phys. B 864

2012

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V. Pestun, “Localization of gauge theory on a four-sphere and supersymmetric Wilson loops,” [arXiv:0712.2824 [hep-th]]

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Y. Imamura and D. Yokoyama, “ 𝒩 = 2 {\cal N}=2 supersymmetric theories on squashed three-sphere,” arXiv:1109.4734 [hep-th]

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D. Gang, “Chern-Simons theory on L(p,q) lens spaces and Localization,” arXiv: 0912.4664 [hep-th]

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D. Martelli and A. Passias, “The gravity dual of supersymmetric gauge theories on a two-parameter deformed three-sphere,” arXiv:1306.3893 [hep-th]

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D. Martelli, A. Passias and J. Sparks, “The supersymmetric NUTs and bolts of holography,” arXiv:1212.4618 [hep-th]

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N. Drukker, T. Okuda and F. Passerini, “Exact results for vortex loop operators in 3d supersymmetric theories,” arXiv:1211.3409 [hep-th]

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