Abstract
We prove that 3d superconformal index for general \( \mathcal{N} \) = 2 U(N) gauge group with fundamentals and anti-fundmentals with/without Chern-Simons terms is factorized into vortex and anti-vortex partition function. We show that for simple cases, 3d vortex partition function coincides with a suitable topological open string partition function. We provide much more elegant derivation at the index level for \( \mathcal{N} \) = 2 Seiberg-like dualities of unitary gauge groups with fundamantal matters and \( \mathcal{N} \) = 4 mirror symmetry
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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].
V. Niarchos, R-charges, chiral rings and RG flows in supersymmetric Chern-Simons-matter theories, JHEP 05 (2009) 054 [arXiv:0903.0435] [INSPIRE].
A. Kapustin, B. Willett and I. Yaakov, Nonperturbative tests of three-dimensional dualities, JHEP 10 (2010) 013 [arXiv:1003.5694] [INSPIRE].
A. Kapustin, B. Willett and I. Yaakov, Tests of Seiberg-like duality in three dimensions, arXiv:1012.4021 [INSPIRE].
D. Bashkirov and A. Kapustin, Dualities between N = 8 superconformal field theories in three dimensions, JHEP 05 (2011) 074 [arXiv:1103.3548] [INSPIRE].
C. Krattenthaler, V.P. Spiridonov and G.S. Vartanov, Superconformal indices of three-dimensional theories related by mirror symmetry, JHEP 06 (2011) 008 [arXiv:1103.4075] [INSPIRE].
D. Jafferis and X. Yin, A duality appetizer, arXiv:1103.5700 [INSPIRE].
A. Kapustin, Seiberg-like duality in three dimensions for orthogonal gauge groups, arXiv:1104.0466 [INSPIRE].
B. Willett and I. Yaakov, N = 2 dualities and Z extremization in three dimensions, arXiv:1104.0487 [INSPIRE].
A. Kapustin and B. Willett, Generalized superconformal index for three dimensional field theories, arXiv:1106.2484 [INSPIRE].
D. Bashkirov, Aharony duality and monopole operators in three dimensions, arXiv:1106.4110 [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].
D. Gang, E. Koh, K. Lee and J. Park, ABCD of 3d \( \mathcal{N} \) = 8 and 4 superconformal field theories, arXiv:1108.3647 [INSPIRE].
D. Berenstein and M. Romo, Monopole operators, moduli spaces and dualities, JHEP 03 (2012) 063 [arXiv:1108.4013] [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].
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].
S. Pasquetti, Factorisation of N = 2 theories on the squashed 3-sphere, JHEP 04 (2012) 120 [arXiv:1111.6905] [INSPIRE].
N. Doroud, J. Gomis, B. Floch and S. Lee, Exact results in D = 2 supersymmetric gauge theories, arXiv:1206.3895.
F. Benini and S. Cremonesi, Partition functions of N = (2, 2) gauge theories on S 2 and vortices, arXiv:1206.2356 [INSPIRE].
T. Dimofte, D. Gaiotto and S. Gukov, 3-manifolds and 3d indices, arXiv:1112.5179 [INSPIRE].
A. Iqbal and C. Vafa, BPS degeneracies and superconformal index in diverse dimensions, arXiv:1210.3605 [INSPIRE].
C. Beem, T. Dimofte and S. Pasquetti, Holomorphic blocks in three dimensions, arXiv:1211.1986 [INSPIRE].
J. Bhattacharya and S. Minwalla, Superconformal indices for N = 6 Chern-Simons theories, JHEP 01 (2009) 014 [arXiv:0806.3251] [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].
H.-C. Kim, J. Kim, S. Kim and K. Lee, Vortices and 3 dimensional dualities, arXiv:1204.3895 [INSPIRE].
T. Dimofte, S. Gukov and L. Hollands, Vortex counting and Lagrangian 3-manifolds, Lett. Math. Phys. 98 (2011) 225 [arXiv:1006.0977] [INSPIRE].
A. Iqbal, C. Kozcaz and C. Vafa, The refined topological vertex, JHEP 10 (2009) 069 [hep-th/0701156] [INSPIRE].
A. Iqbal and A.-K. Kashani-Poor, The vertex on a strip, Adv. Theor. Math. Phys. 10 (2006) 317 [hep-th/0410174] [INSPIRE].
H. Awata and H. Kanno, Changing the preferred direction of the refined topological vertex, J. Geom. Phys. 64 (2013) 91 [arXiv:0903.5383] [INSPIRE].
F. Fucito, J.F. Morales and R. Poghossian, Instantons on quivers and orientifolds, JHEP 10 (2004) 037 [hep-th/0408090] [INSPIRE].
H.-C. Kim and S. Kim, M5-branes from gauge theories on the 5-sphere, JHEP 05 (2013) 144 [arXiv:1206.6339] [INSPIRE].
G. Lockhart and C. Vafa, Superconformal partition functions and non-perturbative topological strings, arXiv:1210.5909 [INSPIRE].
H.-C. Kim, J. Kim and S. Kim, Instantons on the 5-sphere and M5-branes, arXiv:1211.0144 [INSPIRE].
H.-C. Kim, S.-S. Kim and K. Lee, 5-dim superconformal index with enhanced E n global symmetry, JHEP 10 (2012) 142 [arXiv:1206.6781] [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, 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].
D.L. Jafferis, The exact superconformal R-symmetry extremizes Z, JHEP 05 (2012) 159 [arXiv:1012.3210] [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].
H. Jockers, V. Kumar, J.M. Lapan, D.R. Morrison and M. Romo, Two-sphere partition functions and Gromov-Witten invariants, Commun. Math. Phys. 325 (2014) 1139 [arXiv:1208.6244] [INSPIRE].
J. Gomis and S. Lee, Exact Kähler potential from gauge theory and mirror symmetry, JHEP 04 (2013) 019 [arXiv:1210.6022] [INSPIRE].
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Hwang, C., Kim, HC. & Park, J. Factorization of the 3d superconformal index. J. High Energ. Phys. 2014, 18 (2014). https://doi.org/10.1007/JHEP08(2014)018
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DOI: https://doi.org/10.1007/JHEP08(2014)018