Abstract
We extend recent work on the relation of 4d and 3d IR dualities of supersymmetric gauge theories with four supercharges to the case of orthogonal gauge groups. The distinction between different SO(N) gauge theories in 4d plays an important role in this relation. We show that the 4d duality leads to a 3d duality between an SO(N c ) gauge theory with N f flavors and an SO(N f − N c + 2) theory with N f flavors and extra singlets, and we derive its generalization in the presence of Chern-Simons terms. There are two different O(N) theories in 3d, which we denote by O(N)±, and we also show that the O(N c )− gauge theory is dual to a Spin(N f − N c + 2) theory, and derive from 4d the known duality between O(N c )+ and O(N f − N c + 2)+. We verify the consistency of these 3d dualities by various methods, including index computations.
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References
N. Seiberg, Electric-magnetic duality in supersymmetric nonAbelian gauge theories, Nucl. Phys. B 435 (1995) 129 [hep-th/9411149] [INSPIRE].
K.A. Intriligator and N. Seiberg, Duality, monopoles, dyons, confinement and oblique confinement in supersymmetric SO(N c ) gauge theories, Nucl. Phys. B 444 (1995) 125 [hep-th/9503179] [INSPIRE].
K.A. Intriligator and N. Seiberg, Lectures on supersymmetric gauge theories and electric-magnetic duality, Nucl. Phys. Proc. Suppl. 45BC (1996) 1 [hep-th/9509066] [INSPIRE].
M.J. Strassler, Duality, phases, spinors and monopoles in SO(N) and spin(N) gauge theories, JHEP 09 (1998) 017 [hep-th/9709081] [INSPIRE].
O. Aharony, N. Seiberg and Y. Tachikawa, Reading between the lines of four-dimensional gauge theories, arXiv:1305.0318 [INSPIRE].
O. Aharony, S.S. Razamat, N. Seiberg and B. Willett, 3d dualities from 4d dualities, JHEP 07 (2013) 149 [arXiv:1305.3924] [INSPIRE].
V. Niarchos, Seiberg dualities and the 3d/4d connection, JHEP 07 (2012) 075 [arXiv:1205.2086] [INSPIRE].
K.A. Intriligator and N. Seiberg, Phases of N = 1 supersymmetric gauge theories and electric-magnetic triality, hep-th/9506084 [INSPIRE].
D. Gaiotto, G.W. Moore and A. Neitzke, Framed BPS States, arXiv:1006.0146 [INSPIRE].
F. Benini, C. Closset and S. Cremonesi, Comments on 3d Seiberg-like dualities, JHEP 10 (2011) 075 [arXiv:1108.5373] [INSPIRE].
C. Hwang, K.-J. Park and J. Park, Evidence for Aharony duality for orthogonal gauge groups, JHEP 11 (2011) 011 [arXiv:1109.2828] [INSPIRE].
O. Aharony and I. Shamir, On O(N c ) D = 3 N = 2 supersymmetric QCD Theories, JHEP 12 (2011) 043 [arXiv:1109.5081] [INSPIRE].
O. Aharony, A. Hanany, K.A. Intriligator, N. Seiberg and M. Strassler, Aspects of N = 2 supersymmetric gauge theories in three-dimensions, Nucl. Phys. B 499 (1997) 67 [hep-th/9703110] [INSPIRE].
K. Intriligator and N. Seiberg, Aspects of 3d N = 2 Chern-Simons-Matter Theories, arXiv:1305.1633 [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].
N.M. Davies, T.J. Hollowood and V.V. Khoze, Monopoles, affine algebras and the gluino condensate, J. Math. Phys. 44 (2003) 3640 [hep-th/0006011] [INSPIRE].
N. Seiberg and E. Witten, Gauge dynamics and compactification to three-dimensions, hep-th/9607163 [INSPIRE].
N. Seiberg, Exact results on the space of vacua of four-dimensional SUSY gauge theories, Phys. Rev. D 49 (1994) 6857 [hep-th/9402044] [INSPIRE].
K.-M. Lee and P. Yi, Monopoles and instantons on partially compactified D-branes, Phys. Rev. D 56 (1997) 3711 [hep-th/9702107] [INSPIRE].
K.-M. Lee, Instantons and magnetic monopoles on R 3 × S 1 with arbitrary simple gauge groups, Phys. Lett. B 426 (1998) 323 [hep-th/9802012] [INSPIRE].
N.M. Davies, T.J. Hollowood, V.V. Khoze and M.P. Mattis, Gluino condensate and magnetic monopoles in supersymmetric gluodynamics, Nucl. Phys. B 559 (1999) 123 [hep-th/9905015] [INSPIRE].
J.M. Maldacena, G.W. Moore and N. Seiberg, D-brane charges in five-brane backgrounds, JHEP 10 (2001) 005 [hep-th/0108152] [INSPIRE].
T. Banks and N. Seiberg, Symmetries and Strings in Field Theory and Gravity, Phys. Rev. D 83 (2011) 084019 [arXiv:1011.5120] [INSPIRE].
A. Kapustin, Seiberg-like duality in three dimensions for orthogonal gauge groups, arXiv:1104.0466 [INSPIRE].
S.G. Naculich, H. Riggs and H. Schnitzer, Group level duality in wzw models and Chern-Simons theory, Phys. Lett. B 246 (1990) 417 [INSPIRE].
E. Mlawer, S.G. Naculich, H. Riggs and H. Schnitzer, Group level duality of WZW fusion coefficients and Chern-Simons link observables, Nucl. Phys. B 352 (1991) 863 [INSPIRE].
T. Nakanishi and A. Tsuchiya, Level rank duality of WZW models in conformal field theory, Commun. Math. Phys. 144 (1992) 351 [INSPIRE].
O. Aharony, IR duality in D = 3 N = 2 supersymmetric USp(2N c ) and U(N c ) gauge theories, Phys. Lett. B 404 (1997) 71 [hep-th/9703215] [INSPIRE].
K.A. Intriligator and N. Seiberg, Mirror symmetry in three-dimensional gauge theories, Phys. Lett. B 387 (1996) 513 [hep-th/9607207] [INSPIRE].
J. de Boer, K. Hori, H. Ooguri and Y. Oz, Mirror symmetry in three-dimensional gauge theories, quivers and D-branes, Nucl. Phys. B 493 (1997) 101 [hep-th/9611063] [INSPIRE].
J. de Boer, K. Hori, Y. Oz and Z. Yin, Branes and mirror symmetry in N = 2 supersymmetric gauge theories in three-dimensions, Nucl. Phys. B 502 (1997) 107 [hep-th/9702154] [INSPIRE].
D. Green, Z. Komargodski, N. Seiberg, Y. Tachikawa and B. Wecht, Exactly Marginal Deformations and Global Symmetries, JHEP 06 (2010) 106 [arXiv:1005.3546] [INSPIRE].
C. Hwang, H. Kim, K.-J. Park and J. Park, Index computation for 3d Chern-Simons matter theory: test of Seiberg-like duality, JHEP 09 (2011) 037 [arXiv:1107.4942] [INSPIRE].
J. Bhattacharya, S. Bhattacharyya, S. Minwalla and S. Raju, Indices for Superconformal Field Theories in 3,5 and 6 Dimensions, JHEP 02 (2008) 064 [arXiv:0801.1435] [INSPIRE].
S. Kim, The Complete superconformal index for N = 6 Chern-Simons theory, Nucl. Phys. B 821 (2009) 241 [Erratum ibid. B 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].
A. Kapustin and B. Willett, Generalized Superconformal Index for Three Dimensional Field Theories, arXiv:1106.2484 [INSPIRE].
T. Dimofte, D. Gaiotto and S. Gukov, 3-Manifolds and 3d Indices, arXiv:1112.5179 [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].
A. Niemi and G. Semenoff, Axial Anomaly Induced Fermion Fractionization and Effective Gauge Theory Actions in Odd Dimensional Space-Times, Phys. Rev. Lett. 51 (1983) 2077 [INSPIRE].
A. Redlich, Parity Violation and Gauge Noninvariance of the Effective Gauge Field Action in Three-Dimensions, Phys. Rev. D 29 (1984) 2366 [INSPIRE].
B.I. Zwiebel, Charging the Superconformal Index, JHEP 01 (2012) 116 [arXiv:1111.1773] [INSPIRE].
A. Kapustin, Three-dimensional Avatars of Seiberg Duality, talk given at Simons Summer Workshop in Mathematics and Physics 2011, http://media.scgp.stonybrook.edu/video/video.php?f=20110810_1_qtp.mp4.
J. Park and K.-J. Park, Seiberg-like Dualities for 3d N = 2 Theories with SU(N) gauge group, arXiv:1305.6280 [INSPIRE].
F. Dolan, V. Spiridonov and G. Vartanov, From 4d superconformal indices to 3d partition functions, Phys. Lett. B 704 (2011) 234 [arXiv:1104.1787] [INSPIRE].
A. Gadde and W. Yan, Reducing the 4d Index to the S 3 Partition Function, JHEP 12 (2012) 003 [arXiv:1104.2592] [INSPIRE].
Y. Imamura, Relation between the 4d superconformal index and the S 3 partition function, JHEP 09 (2011) 133 [arXiv:1104.4482] [INSPIRE].
G. Felder and A. Varchenko, The elliptic gamma function and SL(3, \( \mathbb{Z} \)) × Z 3, Adv. Math. 156 (2000) 44 [math/9907061].
F. Dolan and H. Osborn, Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N = 1 Dual Theories, Nucl. Phys. B 818 (2009) 137 [arXiv:0801.4947] [INSPIRE].
V. Spiridonov and G. Vartanov, Elliptic hypergeometry of supersymmetric dualities II. Orthogonal groups, knots and vortices, arXiv:1107.5788 [INSPIRE].
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Aharony, O., Razamat, S.S., Seiberg, N. et al. 3d dualities from 4d dualities for orthogonal groups. J. High Energ. Phys. 2013, 99 (2013). https://doi.org/10.1007/JHEP08(2013)099
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DOI: https://doi.org/10.1007/JHEP08(2013)099