Abstract
Localization of supersymmetric \( \mathcal{N} \) = 2 Chern-Simons-Matter theory on a squashed S 3 with SU(2) × U(1) isometry has been studied by different groups of authors. In this paper, we localize the theory on a squashed S 3 with SU(2) × U(1) isometry and a class of complex background. We see that certain kinds of shifts of the background gauge fields are crucial in obtaining nontrivial results, and the previously found results on this manifold can be incorporated in our results as special limits.
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References
E. Witten, Topological quantum field theory, Commun. Math. Phys. 117 (1988) 353.
E. Witten, Two-dimensional gauge theories revisited, J. Geom. Phys. 9 (1992) 303 [hep-th/9204083] [INSPIRE].
N.A. Nekrasov, Seiberg-Witten prepotential from instanton counting, Adv. Theor. Math. Phys. 7 (2004) 831 [hep-th/0206161] [INSPIRE].
V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys. 313 (2012) 71 [arXiv:0712.2824] [INSPIRE].
A. Kapustin, B. Willett and I. Yaakov, Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter, JHEP 03 (2010) 089 [arXiv:0909.4559] [INSPIRE].
D.L. Jafferis, The Exact Superconformal R-Symmetry Extremizes Z, JHEP 05 (2012) 159 [arXiv:1012.3210] [INSPIRE].
N. Hama, K. Hosomichi and S. Lee, Notes on SUSY Gauge Theories on Three-Sphere, JHEP 03 (2011) 127 [arXiv:1012.3512] [INSPIRE].
N. Hama, K. Hosomichi and S. Lee, SUSY Gauge Theories on Squashed Three-Spheres, JHEP 05 (2011) 014 [arXiv:1102.4716] [INSPIRE].
Y. Imamura and D. Yokoyama, N = 2 supersymmetric theories on squashed three-sphere, Phys. Rev. D 85 (2012) 025015 [arXiv:1109.4734] [INSPIRE].
F. Benini and S. Cremonesi, Partition functions of N = (2,2) gauge theories on S 2 and vortices, arXiv:1206.2356 [INSPIRE].
N. Doroud, J. Gomis, B. Le Floch and S. Lee, Exact Results in D = 2 Supersymmetric Gauge Theories, JHEP 05 (2013) 093 [arXiv:1206.2606] [INSPIRE].
J. Gomis and S. Lee, Exact Kähler Potential from Gauge Theory and Mirror Symmetry, JHEP 04 (2013) 019 [arXiv:1210.6022] [INSPIRE].
C. Beem, T. Dimofte and S. Pasquetti, Holomorphic Blocks in Three Dimensions, arXiv:1211.1986 [INSPIRE].
N. Hama and K. Hosomichi, Seiberg-Witten Theories on Ellipsoids, JHEP 09 (2012) 033 [Addendum ibid. 1210 (2012) 051] [arXiv:1206.6359] [INSPIRE].
K. Hosomichi, R.-K. Seong and S. Terashima, Supersymmetric Gauge Theories on the Five-Sphere, Nucl. Phys. B 865 (2012) 376 [arXiv:1203.0371] [INSPIRE].
Y. Imamura, Supersymmetric theories on squashed five-sphere, PTEP 2013 (2013) 013B04 [arXiv:1209.0561] [INSPIRE].
G. Festuccia and N. Seiberg, Rigid Supersymmetric Theories in Curved Superspace, JHEP 06 (2011) 114 [arXiv:1105.0689] [INSPIRE].
C. Klare, A. Tomasiello and A. Zaffaroni, Supersymmetry on Curved Spaces and Holography, JHEP 08 (2012) 061 [arXiv:1205.1062] [INSPIRE].
T.T. Dumitrescu, G. Festuccia and N. Seiberg, Exploring Curved Superspace, JHEP 08 (2012) 141 [arXiv:1205.1115] [INSPIRE].
T.T. Dumitrescu and G. Festuccia, Exploring Curved Superspace (II), JHEP 01 (2013) 072 [arXiv:1209.5408] [INSPIRE].
C. Closset, T.T. Dumitrescu, G. Festuccia and Z. Komargodski, Supersymmetric Field Theories on Three-Manifolds, JHEP 05 (2013) 017 [arXiv:1212.3388] [INSPIRE].
Y. Pan, Rigid Supersymmetry on 5-dimensional Riemannian Manifolds and Contact Geometry, JHEP 05 (2014) 041 [arXiv:1308.1567] [INSPIRE].
S.M. Kuzenko, Symmetries of curved superspace, JHEP 03 (2013) 024 [arXiv:1212.6179] [INSPIRE].
J.H. Schwarz, Superconformal Chern-Simons theories, JHEP 11 (2004) 078 [hep-th/0411077] [INSPIRE].
M.A. Bandres, A.E. Lipstein and J.H. Schwarz, N = 8 Superconformal Chern-Simons Theories, JHEP 05 (2008) 025 [arXiv:0803.3242] [INSPIRE].
D. Martelli and A. Passias, The gravity dual of supersymmetric gauge theories on a two-parameter deformed three-sphere, Nucl. Phys. B 877 (2013) 51 [arXiv:1306.3893] [INSPIRE].
D. Martelli, A. Passias and J. Sparks, The supersymmetric NUTs and bolts of holography, Nucl. Phys. B 876 (2013) 810 [arXiv:1212.4618] [INSPIRE].
L.F. Alday, D. Martelli, P. Richmond and J. Sparks, Localization on Three-Manifolds, JHEP 10 (2013) 095 [arXiv:1307.6848] [INSPIRE].
S.-y. Koyama and N. Kurokawa, Values of the double sine function, J. Number Theory 123 (2007) 204.
S. Pasquetti, Factorisation of N = 2 Theories on the Squashed 3-Sphere, JHEP 04 (2012) 120 [arXiv:1111.6905] [INSPIRE].
D. Martelli and J. Sparks, The gravity dual of supersymmetric gauge theories on a biaxially squashed three-sphere, Nucl. Phys. B 866 (2013) 72 [arXiv:1111.6930] [INSPIRE].
N. Drukker, T. Okuda and F. Passerini, Exact results for vortex loop operators in 3d supersymmetric theories, arXiv:1211.3409 [INSPIRE].
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Nian, J. Localization of supersymmetric Chern-Simons-Matter theory on a squashed S 3 with SU(2) × U(1) isometry. J. High Energ. Phys. 2014, 126 (2014). https://doi.org/10.1007/JHEP07(2014)126
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DOI: https://doi.org/10.1007/JHEP07(2014)126