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Factorization of S^3/Z_n partition function · Around

2013

Factorization of S^3/Z_n partition function

Imamura, Yosuke, Matsuno, Hiroki, Yokoyama, Daisuke

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We investigate S^3/Z_n partition function of 3d N = 2 supersymmetric field theories.

In a gauge theory the partition function is the sum of the contributions of sectors specified by holonomies, and we should carefully choose the relative signs among the contributions.
We argue that the factorization to holomorphic blocks is a useful criterion to determine the signs and propose a formula for them.
We show that the orbifold partition function of a general non-gauge theory is correctly factorized provided that we take appropriate relative signs.

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2012

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V. Pestun, “Localization of gauge theory on a four-sphere and supersymmetric Wilson loops,” Commun. Math. Phys. 313

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2012

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F. A. H. Dolan, V. P. Spiridonov, G. S. Vartanov, “From 4d superconformal indices to 3d partition functions,” [arXiv:1104.1787 [hep-th]]

Cited in the paper.

A. Gadde and W. Yan, “Reducing the 4d Index to the S 3 S^{3} Partition Function,” arXiv:1104.2592 [hep-th]

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Y. Imamura, “Relation between the 4d superconformal index and the S 3 partition function,” [arXiv:1104.4482 [hep-th]]

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L. F. Alday, D. Martelli, P. Richmond and J. Sparks, arXiv:1307.6848 [hep-th]

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J. Nian, “Localization of Supersymmetric Chern-Simons-Matter Theory on a Squashed S 3 S^{3} with S U ( 2 ) × U ⁡ ( 1 ) SU(2)\times U(1) Isometry,” arXiv:1309.3266 [hep-th]

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C. Closset, T. T. Dumitrescu, G. Festuccia and Z. Komargodski, “The Geometry of Supersymmetric Partition Functions,” arXiv:1309.5876 [hep-th]

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2013

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