Abstract
We engineer a brane picture for the reduction of Seiberg dualities from 4D to 3D, valid also in the presence of orientifold planes. We obtain effective 3D dualities on the circle by T-duality, geometrizing the non-perturbative superpotential which is an affine Toda potential. When reducing to pure 3D, we define a double-scaling limit which creates a sector of interacting singlets, giving a unified mechanism for the brane reduction of dualities.
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References
A. Amariti, D. Forcella, C. Klare, D. Orlando and S. Reffert, The braneology of 3D dualities, J. Phys. A 48 (2015) 265401 [arXiv:1501.06571] [INSPIRE].
N. Seiberg, Electric-magnetic duality in supersymmetric nonAbelian gauge theories, Nucl. Phys. B 435 (1995) 129 [hep-th/9411149] [INSPIRE].
A. Karch, Seiberg duality in three-dimensions, Phys. Lett. B 405 (1997) 79 [hep-th/9703172] [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].
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].
O. Aharony, S.S. Razamat, N. Seiberg and B. Willett, 3d dualities from 4d dualities for orthogonal groups, JHEP 08 (2013) 099 [arXiv:1307.0511] [INSPIRE].
A. Hanany and E. Witten, Type IIB superstrings, BPS monopoles and three-dimensional gauge dynamics, Nucl. Phys. B 492 (1997) 152 [hep-th/9611230] [INSPIRE].
A. Hanany and B. Kol, On orientifolds, discrete torsion, branes and M-theory, JHEP 06 (2000) 013 [hep-th/0003025] [INSPIRE].
A. Hanany and J. Troost, Orientifold planes, affine algebras and magnetic monopoles, JHEP 08 (2001) 021 [hep-th/0107153] [INSPIRE].
A. Giveon and D. Kutasov, Seiberg Duality in Chern-Simons Theory, Nucl. Phys. B 812 (2009) 1 [arXiv:0808.0360] [INSPIRE].
V. Niarchos, Seiberg Duality in Chern-Simons Theories with Fundamental and Adjoint Matter, JHEP 11 (2008) 001 [arXiv:0808.2771] [INSPIRE].
D. Orlando and S. Reffert, Relating Gauge Theories via Gauge/ Bethe Correspondence, JHEP 10 (2010) 071 [arXiv:1005.4445] [INSPIRE].
D. Orlando and S. Reffert, The Gauge-Bethe Correspondence and Geometric Representation Theory, Lett. Math. Phys. 98 (2011) 289 [arXiv:1011.6120] [INSPIRE].
B. Willett and I. Yaakov, N = 2 Dualities and Z Extremization in Three Dimensions, arXiv:1104.0487 [INSPIRE].
F. Benini, C. Closset and S. Cremonesi, Comments on 3d Seiberg-like dualities, JHEP 10 (2011) 075 [arXiv:1108.5373] [INSPIRE].
A. Kapustin, H. Kim and J. Park, Dualities for 3d Theories with Tensor Matter, JHEP 12 (2011) 087 [arXiv:1110.2547] [INSPIRE].
H. Kim and J. Park, Aharony Dualities for 3d Theories with Adjoint Matter, JHEP 06 (2013) 106 [arXiv:1302.3645] [INSPIRE].
O. Aharony and D. Fleischer, IR Dualities in General 3d Supersymmetric SU(N ) QCD Theories, JHEP 02 (2015) 162 [arXiv:1411.5475] [INSPIRE].
C. Csáki, M. Martone, Y. Shirman, P. Tanedo and J. Terning, Dynamics of 3D SUSY Gauge Theories with Antisymmetric Matter, JHEP 08 (2014) 141 [arXiv:1406.6684] [INSPIRE].
K. Nii, 3d duality with adjoint matter from 4d duality, JHEP 02 (2015) 024 [arXiv:1409.3230] [INSPIRE].
A. Amariti, A note on 3D N = 2 dualities: real mass flow and partition function, JHEP 03 (2014) 064 [arXiv:1309.6434] [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].
E.J. Weinberg, Fundamental Monopoles and Multi-Monopole Solutions for Arbitrary Simple Gauge Groups, Nucl. Phys. B 167 (1980) 500 [INSPIRE].
E.J. Weinberg, Fundamental Monopoles in Theories With Arbitrary Symmetry Breaking, Nucl. Phys. B 203 (1982) 445 [INSPIRE].
H. Garland and M.K. Murray, Kac-Moody Monopoles and Periodic Instantons, Commun. Math. Phys. 120 (1988) 335 [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].
O. Aharony, A. Hanany, K.A. Intriligator, N. Seiberg and M.J. Strassler, Aspects of N = 2 supersymmetric gauge theories in three-dimensions, Nucl. Phys. B 499 (1997) 67 [hep-th/9703110] [INSPIRE].
K.A. Intriligator and P. Pouliot, Exact superpotentials, quantum vacua and duality in supersymmetric SP (N c ) gauge theories, Phys. Lett. B 353 (1995) 471 [hep-th/9505006] [INSPIRE].
S. Elitzur, A. Giveon, D. Kutasov, E. Rabinovici and A. Schwimmer, Brane dynamics and N =1 supersymmetric gauge theory, Nucl. Phys. B 505 (1997) 202 [hep-th/9704104] [INSPIRE].
K.A. Intriligator, New RG fixed points and duality in supersymmetric SP (N c ) and SO(N c ) gauge theories, Nucl. Phys. B 448 (1995) 187 [hep-th/9505051] [INSPIRE].
R.G. Leigh and M.J. Strassler, Duality of Sp(2N c ) and SO(N c ) supersymmetric gauge theories with adjoint matter, Phys. Lett. B 356 (1995) 492 [hep-th/9505088] [INSPIRE].
K.A. Intriligator, R.G. Leigh and M.J. Strassler, New examples of duality in chiral and nonchiral supersymmetric gauge theories, Nucl. Phys. B 456 (1995) 567 [hep-th/9506148] [INSPIRE].
D. Kutasov, A. Schwimmer and N. Seiberg, Chiral rings, singularity theory and electric-magnetic duality, Nucl. Phys. B 459 (1996) 455 [hep-th/9510222] [INSPIRE].
K. Landsteiner and E. Lopez, New curves from branes, Nucl. Phys. B 516 (1998) 273 [hep-th/9708118] [INSPIRE].
C. Csáki, M. Schmaltz, W. Skiba and J. Terning, Gauge theories with tensors from branes and orientifolds, Phys. Rev. D 57 (1998) 7546 [hep-th/9801207] [INSPIRE].
J.H. Brodie and A. Hanany, Type IIA superstrings, chiral symmetry and N = 1 4D gauge theory dualities, Nucl. Phys. B 506 (1997) 157 [hep-th/9704043] [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].
O. Aharony, N. Seiberg and Y. Tachikawa, Reading between the lines of four-dimensional gauge theories, JHEP 08 (2013) 115 [arXiv:1305.0318] [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].
A. Hanany and A. Zaffaroni, Chiral symmetry from type IIA branes, Nucl. Phys. B 509 (1998) 145 [hep-th/9706047] [INSPIRE].
A. Hanany and A. Zaffaroni, On the realization of chiral four-dimensional gauge theories using branes, JHEP 05 (1998) 001 [hep-th/9801134] [INSPIRE].
A. Hanany and A. Zaffaroni, Issues on orientifolds: On the brane construction of gauge theories with SO(2N ) global symmetry, JHEP 07 (1999) 009 [hep-th/9903242] [INSPIRE].
G.W. Moore, A.B. Royston and D. Van den Bleeken, Brane bending and monopole moduli, JHEP 10 (2014) 157 [arXiv:1404.7158] [INSPIRE].
M.K. Benna, I.R. Klebanov and T. Klose, Charges of Monopole Operators in Chern-Simons Yang-Mills Theory, JHEP 01 (2010) 110 [arXiv:0906.3008] [INSPIRE].
C. Romelsberger, Counting chiral primaries in N = 1, D = 4 superconformal field theories, Nucl. Phys. B 747 (2006) 329 [hep-th/0510060] [INSPIRE].
J. Kinney, J.M. Maldacena, S. Minwalla and S. Raju, An index for 4 dimensional super conformal theories, Commun. Math. Phys. 275 (2007) 209 [hep-th/0510251] [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].
A. Amariti and C. Klare, A journey to 3d: exact relations for adjoint SQCD from dimensional reduction, JHEP 05 (2015) 148 [arXiv:1409.8623] [INSPIRE].
I.B. Gahramanov and G.S. Vartanov, Superconformal indices and partition functions for supersymmetric field theories, arXiv:1310.8507 [INSPIRE].
V.P. Spiridonov and G.S. Vartanov, Elliptic Hypergeometry of Supersymmetric Dualities, Commun. Math. Phys. 304 (2011) 797 [arXiv:0910.5944] [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].
A. Sagnotti, Open Strings and their Symmetry Groups, hep-th/0208020 [INSPIRE].
P. Hořava, Strings on World Sheet Orbifolds, Nucl. Phys. B 327 (1989) 461 [INSPIRE].
J. Polchinski, TASI lectures on D-branes, hep-th/9611050 [INSPIRE].
E.G. Gimon and J. Polchinski, Consistency conditions for orientifolds and d manifolds, Phys. Rev. D 54 (1996) 1667 [hep-th/9601038] [INSPIRE].
E. Witten, Baryons and branes in anti-de Sitter space, JHEP 07 (1998) 006 [hep-th/9805112] [INSPIRE].
A.M. Uranga, Towards mass deformed N = 4 SO(N ) and Sp(k) gauge theories from brane configurations, Nucl. Phys. B 526 (1998) 241 [hep-th/9803054] [INSPIRE].
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Amariti, A., Forcella, D., Klare, C. et al. 4D/3D reduction of dualities: mirrors on the circle. J. High Energ. Phys. 2015, 48 (2015). https://doi.org/10.1007/JHEP10(2015)048
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DOI: https://doi.org/10.1007/JHEP10(2015)048