Abstract
We study the IR phases of 3D class R theories associated with closed non-hyperbolic 3-manifolds. Non-hyperbolic 3-manifolds can be obtained by performing Dehn fillings on 1-cusped hyperbolic 3-manifolds along exceptional slopes. In 3D-3D correspondence, the ‘exceptional’ Dehn filling corresponds to the gauging of an SU(2) flavor symmetry in a superconformal field theory associated with a 1-cusped 3-manifold with ‘small’ Chern-Simons levels. With several explicit examples, we analyze various interesting non-perturbative IR phenomena (such as spontaneous SUSY breaking, generation of mass gap and supersymmetry enhancement) from the ‘exceptional’ gaugings. Interestingly, distinguished features of the IR phases can be captured by simple topological properties of non-hyperbolic 3-manifolds. We also find that 3D class R theories associated with certain classes of atoroidal non-hyperbolic 3-manifolds always exhibit supersymmetry enhancement at low energy and actually flow to 3D rank-0 \( \mathcal{N} \) = 4 SCFTs with trivial vacuum moduli space.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D. Gaiotto, N = 2 dualities, JHEP 08 (2012) 034 [arXiv:0904.2715] [INSPIRE].
D. Gaiotto, G.W. Moore and A. Neitzke, Wall-crossing, Hitchin systems, and the WKB approximation, Adv. Math. 234 (2013) 239 [arXiv:0907.3987] [INSPIRE].
Y. Terashima and M. Yamazaki, SL(2, R) Chern-Simons, Liouville, and Gauge Theory on Duality Walls, JHEP 08 (2011) 135 [arXiv:1103.5748] [INSPIRE].
T. Dimofte, D. Gaiotto and S. Gukov, Gauge Theories Labelled by Three-Manifolds, Commun. Math. Phys. 325 (2014) 367 [arXiv:1108.4389] [INSPIRE].
T. Dimofte, D. Gaiotto and S. Gukov, 3-Manifolds and 3d Indices, Adv. Theor. Math. Phys. 17 (2013) 975 [arXiv:1112.5179] [INSPIRE].
G.Y. Cho, D. Gang and H.-C. Kim, M-theoretic Genesis of Topological Phases, JHEP 11 (2020) 115 [arXiv:2007.01532] [INSPIRE].
D. Gang, S. Kim, K. Lee, M. Shim and M. Yamazaki, Non-unitary TQFTs from 3D \( \mathcal{N} \) = 4 rank 0 SCFTs, JHEP 08 (2021) 158 [arXiv:2103.09283] [INSPIRE].
N.M. Dunfield, A census of exceptional Dehn fillings, arXiv:1812.11940.
M. Culler, N.M. Dunfield, M. Goerner and J.R. Weeks, SnapPy, a computer program for studying the geometry and topology of 3-manifolds, http://snappy.computop.org.
W.P. Thurston, Three-dimensional geometry and topology, Volume 1, Princeton university press (2014) [DOI].
W. Jaco and P.B. Shalen, Seifert fibered spaces in 3-manifolds, in Geometric topology, Elsevier (1979), pp. 91–99 [DOI].
K. Johannson, Homotopy equivalences of 3-manifolds with boundaries, Lecture Notes in Mathematics 761, Springer (2006) [DOI].
D. Gang and K. Yonekura, Symmetry enhancement and closing of knots in 3d/3d correspondence, JHEP 07 (2018) 145 [arXiv:1803.04009] [INSPIRE].
D. Gang, Quantum Approach to Dehn Surgery Problem, arXiv:1803.11143 [INSPIRE].
S.X. Cui, Y. Qiu and Z. Wang, From Three Dimensional Manifolds to Modular Tensor Categories, arXiv:2101.01674 [INSPIRE].
S.X. Cui, P. Gustafson, Y. Qiu and Q. Zhang, From Torus Bundles to Particle-Hole Equivariantization, Lett. Math. Phys. 112 (2022) 15 [arXiv:2106.01959] [INSPIRE].
S. Garoufalidis, C.D. Hodgson, J.H. Rubinstein and H. Segerman, 1-efficient triangulations and the index of a cusped hyperbolic 3-manifold, arXiv:1303.5278 [INSPIRE].
S. Garoufalidis, C. Hodgson, N. Hoffman and H. Rubinstein, The 3D-index and normal surfaces, arXiv:1604.02688 [INSPIRE].
D. Gang, H. Kang, G. Kim and H.-C. Kim, TQFTs from SOL/Seifert-fibered manifolds, to appear.
T.D. Dimofte and S. Garoufalidis, The Quantum content of the gluing equations, Geom. Topol. 17 (2013) 1253 [arXiv:1202.6268] [INSPIRE].
D. Gang, M. Romo and M. Yamazaki, All-Order Volume Conjecture for Closed 3-Manifolds from Complex Chern-Simons Theory, Commun. Math. Phys. 359 (2018) 915 [arXiv:1704.00918] [INSPIRE].
A. Gadde, S. Gukov and P. Putrov, Walls, Lines, and Spectral Dualities in 3d Gauge Theories, JHEP 05 (2014) 047 [arXiv:1302.0015] [INSPIRE].
C. Beem, T. Dimofte and S. Pasquetti, Holomorphic Blocks in Three Dimensions, JHEP 12 (2014) 177 [arXiv:1211.1986] [INSPIRE].
H.-J. Chung, T. Dimofte, S. Gukov and P. Sułkowski, 3d-3d Correspondence Revisited, JHEP 04 (2016) 140 [arXiv:1405.3663] [INSPIRE].
D. Pei and K. Ye, A 3d-3d appetizer, JHEP 11 (2016) 008 [arXiv:1503.04809] [INSPIRE].
S. Gukov, D. Pei, P. Putrov and C. Vafa, BPS spectra and 3-manifold invariants, J. Knot Theor. Ramifications 29 (2020) 2040003 [arXiv:1701.06567] [INSPIRE].
J. Eckhard, H. Kim, S. Schäfer-Nameki and B. Willett, Higher-Form Symmetries, Bethe Vacua, and the 3d-3d Correspondence, JHEP 01 (2020) 101 [arXiv:1910.14086] [INSPIRE].
T. Dimofte, S. Gukov and L. Hollands, Vortex Counting and Lagrangian 3-manifolds, Lett. Math. Phys. 98 (2011) 225 [arXiv:1006.0977] [INSPIRE].
S. Kim, The Complete superconformal index for N = 6 Chern-Simons theory, Nucl. Phys. B 821 (2009) 241 [Erratum ibid. 864 (2012) 884] [arXiv:0903.4172] [INSPIRE].
Y. Imamura and S. Yokoyama, Index for three dimensional superconformal field theories with general R-charge assignments, JHEP 04 (2011) 007 [arXiv:1101.0557] [INSPIRE].
D.L. Jafferis, The Exact Superconformal R-Symmetry Extremizes Z, JHEP 05 (2012) 159 [arXiv:1012.3210] [INSPIRE].
S.S. Razamat and B. Willett, Down the rabbit hole with theories of class , JHEP 10 (2014) 099 [arXiv:1403.6107] [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 \( \mathcal{N} \) = 2 theories, JHEP 11 (2018) 004 [arXiv:1807.02328] [INSPIRE].
S. Gukov and D. Pei, Equivariant Verlinde formula from fivebranes and vortices, Commun. Math. Phys. 355 (2017) 1 [arXiv:1501.01310] [INSPIRE].
F. Benini and A. Zaffaroni, A topologically twisted index for three-dimensional supersymmetric theories, JHEP 07 (2015) 127 [arXiv:1504.03698] [INSPIRE].
F. Benini and A. Zaffaroni, Supersymmetric partition functions on Riemann surfaces, Proc. Symp. Pure Math. 96 (2017) 13 [arXiv:1605.06120] [INSPIRE].
C. Closset and H. Kim, Comments on twisted indices in 3d supersymmetric gauge theories, JHEP 08 (2016) 059 [arXiv:1605.06531] [INSPIRE].
H.-C. Kim and S. Kim, Supersymmetric vacua of mass-deformed M2-brane theory, Nucl. Phys. B 839 (2010) 96 [arXiv:1001.3153] [INSPIRE].
K. Intriligator and N. Seiberg, Aspects of 3d N = 2 Chern-Simons-Matter Theories, JHEP 07 (2013) 079 [arXiv:1305.1633] [INSPIRE].
N. Hama, K. Hosomichi and S. Lee, SUSY Gauge Theories on Squashed Three-Spheres, JHEP 05 (2011) 014 [arXiv:1102.4716] [INSPIRE].
L.D. Faddeev and R.M. Kashaev, Quantum Dilogarithm, Mod. Phys. Lett. A 9 (1994) 427 [hep-th/9310070] [INSPIRE].
D. Gang and M. Yamazaki, Expanding 3d \( \mathcal{N} \) = 2 theories around the round sphere, JHEP 02 (2020) 102 [arXiv:1912.09617] [INSPIRE].
E. Witten, Quantum Field Theory and the Jones Polynomial, Commun. Math. Phys. 121 (1989) 351 [INSPIRE].
C. Cordova, T.T. Dumitrescu and K. Intriligator, Multiplets of Superconformal Symmetry in Diverse Dimensions, JHEP 03 (2019) 163 [arXiv:1612.00809] [INSPIRE].
F. Benini and S. Benvenuti, \( \mathcal{N} \) = 1 dualities in 2 + 1 dimensions, JHEP 11 (2018) 197 [arXiv:1803.01784] [INSPIRE].
D. Gaiotto, Z. Komargodski and J. Wu, Curious Aspects of Three-Dimensional \( \mathcal{N} \) = 1 SCFTs, JHEP 08 (2018) 004 [arXiv:1804.02018] [INSPIRE].
D. Jafferis and X. Yin, A Duality Appetizer, arXiv:1103.5700 [INSPIRE].
D. Gang and M. Yamazaki, Three-dimensional gauge theories with supersymmetry enhancement, Phys. Rev. D 98 (2018) 121701 [arXiv:1806.07714] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2206.11982
Rights and permissions
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.
About this article
Cite this article
Choi, S., Gang, D. & Kim, HC. Infrared phases of 3D class R theories. J. High Energ. Phys. 2022, 151 (2022). https://doi.org/10.1007/JHEP11(2022)151
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2022)151