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2012

4d partition function on S^1 x S^3 and 2d Yang-Mills with nonzero area

Tachikawa, Yuji

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We argue that 6d N=(2,0) theory on S^1 x S^3 x C_2 reduces to the 2d q-deformed Yang-Mills on C_2 at finite area, as a small extension to the result of Gadde, Rastelli, Razamat and Yan.

This is done by computing the partition function on S^1 x S^3 of 4d N=2 supersymmetric non-linear sigma model on T^*G_C, which gives the propagator of the 2d Yang-Mills.

4d partition function on S^1 x S^3 and 2d Yang-Mills with nonzero area · Around

Built on

J. Källén and M. Zabzine, “Twisted Supersymmetric 5D Yang-Mills Theory and Contact Geometry,”
Original
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C. Pedder, J. Sonner, and D. Tong, “The Geometric Phase in Supersymmetric Quantum Mechanics,”
Original
2008
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J. Sonner and D. Tong, “Berry Phase and Supersymmetry,”
Original
2009
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Similar

A. Gadde, E. Pomoni, L. Rastelli, and S. S. Razamat, “S-Duality and 2d Topological QFT,”
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2010
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A. Kapustin, B. Willett, and I. Yaakov, “Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter,”
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L. F. Alday, D. Gaiotto, and Y. Tachikawa, “Liouville Correlation Functions from Four-Dimensional Gauge Theories,”
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2010
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A. Gadde, L. Rastelli, S. S. Razamat, and W. Yan, “The 4d Superconformal Index from q-Deformed 2d Yang- Mills,”
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2011
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A. Gadde, L. Rastelli, S. S. Razamat, and W. Yan, “Gauge Theories and Macdonald Polynomials,”
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Cited in the paper.
D. Gaiotto, “
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D. Gaiotto, G. W. Moore, and Y. Tachikawa, “On 6d
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F. Benini and S. Cremonesi, “Partition Functions of
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N. Doroud, J. Gomis, B. Le Floch, and S. Lee, “Exact Results in
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V. Pestun, “Localization of Gauge Theory on a Four-Sphere and Supersymmetric Wilson Loops,”
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K. Hosomichi, R.-K. Seong, and S. Terashima, “Supersymmetric Gauge Theories on the Five-Sphere,”
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Cited in the paper.
J. Källén, J. Qiu, and M. Zabzine, “The Perturbative Partition Function of Supersymmetric 5D Yang-Mills Theory with Matter on the Five-Sphere,”
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Cited in the paper.

Then

G. Festuccia and N. Seiberg, “Rigid Supersymmetric Theories in Curved Superspace,”
Original
2011
Later among the works it cites.
N. Hama, K. Hosomichi, and S. Lee, “Notes on SUSY Gauge Theories on Three-Sphere,”
Original
2011
Later among the works it cites.
N. Hama, K. Hosomichi, and S. Lee, “SUSY Gauge Theories on Squashed Three-Spheres,”
Original
2011
Later among the works it cites.
Y. Imamura and D. Yokoyama, “
Original
2012
Closest in time.

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