Abstract
In this note we elaborate on the reduction of four dimensional Seiberg duality with adjoint matter to three dimensions. We use the exact formulation of the superconformal index and of the partition function as instruments to test this reduction. We translate the identity between indices of the dual 4d theories to 3d. This produces various new identities between partition functions of 3d dual phases.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
O. Aharony, S.S. Razamat, N. Seiberg and B. Willett, 3d dualities from 4d dualities, JHEP 07 (2013) 149 [arXiv:1305.3924] [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].
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].
A. Karch, Seiberg duality in three-dimensions, Phys. Lett. B 405 (1997) 79 [hep-th/9703172] [INSPIRE].
A. Giveon and D. Kutasov, Seiberg duality in Chern-Simons theory, Nucl. Phys. B 812 (2009) 1 [arXiv:0808.0360] [INSPIRE].
F. Benini, C. Closset and S. Cremonesi, Comments on 3D Seiberg-like dualities, JHEP 10 (2011) 075 [arXiv:1108.5373] [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].
D. Kutasov, A comment on duality in N = 1 supersymmetric non-Abelian gauge theories, Phys. Lett. B 351 (1995) 230 [hep-th/9503086] [INSPIRE].
D. Kutasov and A. Schwimmer, On duality in supersymmetric Yang-Mills theory, Phys. Lett. B 354 (1995) 315 [hep-th/9505004] [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. Nii, 3D duality with adjoint matter from 4D duality, JHEP 02 (2015) 024 [arXiv:1409.3230] [INSPIRE].
H. Kim and J. Park, Aharony dualities for 3D theories with adjoint matter, JHEP 06 (2013) 106 [arXiv:1302.3645] [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].
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].
F.A. 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.P. Spiridonov and G.S. Vartanov, Superconformal indices for N = 1 theories with multiple duals, Nucl. Phys. B 824 (2010) 192 [arXiv:0811.1909] [INSPIRE].
V.P. Spiridonov and G.S. Vartanov, Elliptic hypergeometry of supersymmetric dualities, Commun. Math. Phys. 304 (2011) 797 [arXiv:0910.5944] [INSPIRE].
B. Willett and I. Yaakov, N = 2 dualities and Z extremization in three dimensions, arXiv:1104.0487 [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].
E.M. Rains, Transformations of elliptic hypergometric integrals, math/0309252.
V.P. Spiridonov, On the elliptic Beta function, Russ. Math Surv. 56 (2001) 185.
F. van de Bult, Hyperbolic hypergeometric functions, thesis, Thomas Stieltjes Institute for Mathematics, The Netherlands (2008).
V. Niarchos, Seiberg duality in Chern-Simons theories with fundamental and adjoint matter, JHEP 11 (2008) 001 [arXiv:0808.2771] [INSPIRE].
V. Niarchos, R-charges, chiral rings and RG flows in supersymmetric Chern-Simons-matter theories, JHEP 05 (2009) 054 [arXiv:0903.0435] [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. Seiberg and E. Witten, Gauge dynamics and compactification to three-dimensions, hep-th/9607163 [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].
A. Amariti and C. Klare, Chern-Simons and RG flows: contact with dualities, JHEP 08 (2014) 144 [arXiv:1405.2312] [INSPIRE].
F.A.H. Dolan, V.P. Spiridonov and G.S. 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].
V. Niarchos, Seiberg dualities and the 3d/4d connection, JHEP 07 (2012) 075 [arXiv:1205.2086] [INSPIRE].
P. Agarwal, A. Amariti and M. Siani, Refined checks and exact dualities in three dimensions, JHEP 10 (2012) 178 [arXiv:1205.6798] [INSPIRE].
D. Jafferis and X. Yin, A duality appetizer, arXiv:1103.5700 [INSPIRE].
A. Kapustin, H. Kim and J. Park, Dualities for 3d theories with tensor matter, JHEP 12 (2011) 087 [arXiv:1110.2547] [INSPIRE].
Y. Imamura and D. Yokoyama, S 3 /Z n partition function and dualities, JHEP 11 (2012) 122 [arXiv:1208.1404] [INSPIRE].
J. Park and K.-J. Park, Seiberg-like dualities for 3d N = 2 theories with SU(N) gauge group, JHEP 10 (2013) 198 [arXiv:1305.6280] [INSPIRE].
K. Intriligator and N. Seiberg, Aspects of 3d N = 2 Chern-Simons-matter theories, JHEP 07 (2013) 079 [arXiv:1305.1633] [INSPIRE].
S. Khan and R. Tatar, Flows between dualities for 3d Chern-Simons theories, Phys. Rev. D 88 (2013) 066011 [arXiv:1307.4640] [INSPIRE].
A. Amariti, A note on 3D \( \mathcal{N}=2 \) dualities: real mass flow and partition function, JHEP 03 (2014) 064 [arXiv:1309.6434] [INSPIRE].
J.H. Brodie, Duality in supersymmetric SU(N c ) gauge theory with two adjoint chiral superfields, Nucl. Phys. B 478 (1996) 123 [hep-th/9605232] [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: 1409.8623
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, 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 license, and indicate if changes were made.
About this article
Cite this article
Amariti, A., Klare, C. A journey to 3d: exact relations for adjoint SQCD from dimensional reduction. J. High Energ. Phys. 2015, 148 (2015). https://doi.org/10.1007/JHEP05(2015)148
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2015)148