Abstract
Three dimensional supersymmetric gauge theories are often in a gapped phase, in which SUSY is spontaneously broken, if all the matter fields are massive and decoupled in the low energy. We study this phase in the large N limit using the localization technique for the theory on the ellipsoid, which interpolates the round three sphere and the flat space compactified on S1. We find a large N saddle point solution for the gauge theory with some massive matter fields. This solution gives a vanishing (generalized) Polyakov loop in the flat space limit, thus, it corresponds to the confining phase at the leading order in the 1/N expansion.
Article PDF
Similar content being viewed by others
References
V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys. 313 (2012) 71 [arXiv:0712.2824] [INSPIRE].
E. Witten, Topological quantum field theory, Commun. Math. Phys. 117 (1988) 353 [INSPIRE].
N.A. Nekrasov, Seiberg-Witten prepotential from instanton counting, Adv. Theor. Math. Phys. 7 (2003) 831 [hep-th/0206161] [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].
K. Intriligator and N. Seiberg, Aspects of 3d N = 2 Chern-Simons-matter theories, JHEP 07 (2013) 079 [arXiv:1305.1633] [INSPIRE].
E. Witten, Supersymmetric index of three-dimensional gauge theory, in The many faces of the superworld, M.A. Shifman ed., World Scientific, Singapore, (2000), pg. 156 [hep-th/9903005] [INSPIRE].
K. Ohta, Supersymmetric index and s rule for type IIB branes, JHEP 10 (1999) 006 [hep-th/9908120] [INSPIRE].
T. Nosaka, K. Shimizu and S. Terashima, Mass deformed ABJM theory on three sphere in large N limit, JHEP 03 (2017) 121 [arXiv:1608.02654] [INSPIRE].
M. Honda, T. Nosaka, K. Shimizu and S. Terashima, Supersymmetry breaking in a large N gauge theory with gravity dual, arXiv:1807.08874 [INSPIRE].
T. Nosaka, K. Shimizu and S. Terashima, Large N behavior of mass deformed ABJM theory, JHEP 03 (2016) 063 [arXiv:1512.00249] [INSPIRE].
N. Hama, K. Hosomichi and S. Lee, SUSY gauge theories on squashed three-spheres, JHEP 05 (2011) 014 [arXiv:1102.4716] [INSPIRE].
A. Kapustin, B. Willett and I. Yaakov, Nonperturbative tests of three-dimensional dualities, JHEP 10 (2010) 013 [arXiv:1003.5694] [INSPIRE].
K. Hosomichi, A review on SUSY gauge theories on S 3, in New dualities of supersymmetric gauge theories, Springer, Cham, Switzerland, (2015), pg. 307 [arXiv:1412.7128] [INSPIRE].
A.G. Bytsko and J. Teschner, Quantization of models with non-compact quantum group symmetry: modular XXZ magnet and lattice sinh-Gordon model, J. Phys. A 39 (2006) 12927 [hep-th/0602093] [INSPIRE].
Y. Hatsuda, ABJM on ellipsoid and topological strings, JHEP 07 (2016) 026 [arXiv:1601.02728] [INSPIRE].
C. Closset, H. Kim and B. Willett, Supersymmetric partition functions and the three-dimensional A-twist, JHEP 03 (2017) 074 [arXiv:1701.03171] [INSPIRE].
C. Closset, H. Kim and B. Willett, Seifert fibering operators in 3d N = 2 theories, arXiv:1807.02328 [INSPIRE].
I. Affleck, J.A. Harvey and E. Witten, Instantons and (super)symmetry breaking in (2 + 1)-dimensions, Nucl. Phys. B 206 (1982) 413 [INSPIRE].
T. Morita and V. Niarchos, F-theorem, duality and SUSY breaking in one-adjoint Chern-Simons-matter theories, Nucl. Phys. B 858 (2012) 84 [arXiv:1108.4963] [INSPIRE].
T. Suyama, Supersymmetry breaking and planar free energy in Chern-Simons-matter theories, arXiv:1405.7469 [INSPIRE].
K. Hosomichi, K.-M. Lee, S. Lee, S. Lee and J. Park, N = 5, 6 superconformal Chern-Simons theories and M 2-branes on orbifolds, JHEP 09 (2008) 002 [arXiv:0806.4977] [INSPIRE].
J. Gomis, D. Rodriguez-Gomez, M. Van Raamsdonk and H. Verlinde, A massive study of M 2-brane proposals, JHEP 09 (2008) 113 [arXiv:0807.1074] [INSPIRE].
R.C. Myers, Dielectric branes, JHEP 12 (1999) 022 [hep-th/9910053] [INSPIRE].
Y. Imamura and D. Yokoyama, N = 2 supersymmetric theories on squashed three-sphere, Phys. Rev. D 85 (2012) 025015 [arXiv:1109.4734] [INSPIRE].
C. Toldo and B. Willett, Partition functions on 3d circle bundles and their gravity duals, JHEP 05 (2018) 116 [arXiv:1712.08861] [INSPIRE].
D. Gang and N. Kim, Large N twisted partition functions in 3d-3d correspondence and holography, arXiv:1808.02797 [INSPIRE].
D. Gaiotto and E. Witten, Supersymmetric boundary conditions in N = 4 super Yang-Mills theory, J. Statist. Phys. 135 (2009) 789 [arXiv:0804.2902] [INSPIRE].
C. Closset, T.T. Dumitrescu, G. Festuccia, Z. Komargodski and N. Seiberg, Contact terms, unitarity and F-maximization in three-dimensional superconformal theories, JHEP 10 (2012) 053 [arXiv:1205.4142] [INSPIRE].
C. Closset, T.T. Dumitrescu, G. Festuccia, Z. Komargodski and N. Seiberg, Comments on Chern-Simons contact terms in three dimensions, JHEP 09 (2012) 091 [arXiv:1206.5218] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1809.03670
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Shimizu, K., Terashima, S. Supersymmetry breaking phase in three dimensional large N gauge theories. J. High Energ. Phys. 2018, 64 (2018). https://doi.org/10.1007/JHEP11(2018)064
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2018)064