Abstract
We discuss 3d\( \mathcal{N} \) = 1 supersymmetric SU(N) and U(N) Chern-Simons-matter theories, with Nf matter superfields in the fundamental representation of SU(N) or U(N). In the large N ’t Hooft limit with fixed ’t Hooft coupling λ these theories have one (for Nf = 1) or two (for Nf> 1) exactly marginal deformations in the superpotential. At finite N these couplings acquire a beta function. We compute the beta function exactly for λ = 0, at leading order in 1/N. For Nf = 1 we find four fixed points, one of which is triply-degenerate. We show that at large N there are at most six fixed points for any λ, and conjecture that there are exactly six, with three of them stable (including a point with enhanced \( \mathcal{N} \) = 2 supersymmetry). The strong-weak coupling dualities of \( \mathcal{N} \) = 1 Chern-Simons-matter theories map each of these fixed points to a dual one. We show that at large N the phase structure near each of the three stable fixed points is different. For Nf> 1 we analyze the fixed points at weak coupling, and we work out the action of the strong-weak coupling duality on the marginal and relevant superpotential couplings at large N (which was previously known only for Nf = 1). In addition, we compute in these theories the 2-point and 3-point functions of the lowest gauge-invariant singlet superfield at large N, for all values of λ and of the superpotential couplings, and use them to test the large N dualities. This computation is one of the ingredients needed for a computation of the beta function at order 1/N for all λ, which we leave for future work. We also discuss Chern-Simons-matter theories with extra Hubbard-Stratonovich type singlet fields, and suggest dualities between them.
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References
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, JHEP10 (2011) 075 [arXiv:1108.5373] [INSPIRE].
O. Aharony, S.S. Razamat, N. Seiberg and B. Willett, 3d dualities from 4d dualities, JHEP07 (2013) 149 [arXiv:1305.3924] [INSPIRE].
O. Aharony and D. Fleischer, IR dualities in general 3d supersymmetric SU(N) QCD theories, JHEP02 (2015) 162 [arXiv:1411.5475] [INSPIRE].
O. Aharony, S. Jain and S. Minwalla, Flows, fixed points and duality in Chern-Simons-Matter theories, JHEP12 (2018) 058 [arXiv:1808.03317] [INSPIRE].
L.V. Avdeev, G.V. Grigorev and D.I. Kazakov, Renormalizations in abelian Chern-Simons field theories with matter, Nucl. Phys.B 382 (1992) 561 [INSPIRE].
L.V. Avdeev, D.I. Kazakov and I.N. Kondrashuk, Renormalizations in supersymmetric and nonsupersymmetric nonAbelian Chern-Simons field theories with matter, Nucl. Phys.B 391 (1993) 333 [INSPIRE].
S. Giombi et al., Chern-Simons theory with vector fermion matter, Eur. Phys. J.C 72 (2012) 2112 [arXiv:1110.4386] [INSPIRE].
O. Aharony, G. Gur-Ari and R. Yacoby, d = 3 bosonic vector models coupled to Chern-Simons gauge theories, JHEP03 (2012) 037 [arXiv:1110.4382] [INSPIRE].
O. Aharony, G. Gur-Ari and R. Yacoby, Correlation functions of large N Chern-Simons-Matter theories and bosonization in three dimensions, JHEP12 (2012) 028 [arXiv:1207.4593] [INSPIRE].
S. Jain, S.P. Trivedi, S.R. Wadia and S. Yokoyama, Supersymmetric Chern-Simons theories with vector matter, JHEP10 (2012) 194 [arXiv:1207.4750] [INSPIRE].
O. Aharony et al., The thermal free energy in large N Chern-Simons-Matter theories, JHEP03 (2013) 121 [arXiv:1211.4843] [INSPIRE].
G. Gur-Ari and R. Yacoby, Correlators of large N fermionic Chern-Simons vector models, JHEP02 (2013) 150 [arXiv:1211.1866] [INSPIRE].
S. Jain, S. Minwalla and S. Yokoyama, Chern Simons duality with a fundamental boson and fermion, JHEP11 (2013) 037 [arXiv:1305.7235] [INSPIRE].
K. Inbasekar et al., Unitarity, crossing symmetry and duality in the scattering of \( \mathcal{N} \) = 1 SUSY matter Chern-Simons theories, JHEP10 (2015) 176 [arXiv:1505.06571] [INSPIRE].
S. Choudhury et al., Bose-Fermi Chern-Simons dualities in the Higgsed phase, JHEP11 (2018) 177 [arXiv:1804.08635] [INSPIRE].
A. Dey et al., Duality and an exact Landau-Ginzburg potential for quasi-bosonic Chern-Simons-Matter theories, JHEP11 (2018) 020 [arXiv:1808.04415] [INSPIRE].
D. Gaiotto, Z. Komargodski and J. Wu, Curious Aspects of Three-Dimensional \( \mathcal{N} \) = 1 SCFTs, JHEP08 (2018) 004 [arXiv:1804.02018] [INSPIRE].
M. Gremm and E. Katz, Mirror symmetry for N = 1 QED in three-dimensions, JHEP02 (2000) 008 [hep-th/9906020] [INSPIRE].
J. Gomis, Z. Komargodski and N. Seiberg, Phases of adjoint QCD 3and dualities, SciPost Phys.5 (2018) 007 [arXiv:1710.03258] [INSPIRE].
V. Bashmakov, J. Gomis, Z. Komargodski and A. Sharon, Phases of \( \mathcal{N} \) = 1 theories in 2 + 1 dimensions, JHEP07 (2018) 123 [arXiv:1802.10130] [INSPIRE].
F. Benini and S. Benvenuti, \( \mathcal{N} \) = 1 dualities in 2 + 1 dimensions, JHEP11 (2018) 197 [arXiv:1803.01784] [INSPIRE].
J. Eckhard, S. Schäfer-Nameki and J.-M. Wong, An \( \mathcal{N} \) = 1 3d-3d correspondence, JHEP07 (2018) 052 [arXiv:1804.02368] [INSPIRE].
F. Benini and S. Benvenuti, N = 1 QED in 2 + 1 dimensions: dualities and enhanced symmetries, arXiv:1804.05707 [INSPIRE].
C. Choi, M. Roček and A. Sharon, Dualities and phases of 3D N = 1 SQCD, JHEP10 (2018) 105 [arXiv:1808.02184] [INSPIRE].
A. Dey, I. Halder, S. Jain, S. Minwalla and N. Prabhakar, The large N phase diagram of \( \mathcal{N} \) = 2 SU(N) Chern-Simons theory with one fundamental chiral multiplet, arXiv:1904.07286 [INSPIRE].
B.S. Acharya and C. Vafa, On domain walls of N = 1 supersymmetric Yang-Mills in four-dimensions, hep-th/0103011 [INSPIRE].
V. Bashmakov, F. Benini, S. Benvenuti and M. Bertolini, Living on the walls of super-QCD, SciPost Phys.6 (2019) 044 [arXiv:1812.04645] [INSPIRE].
K. Inbasekar et al., Correlation functions in N = 2 supersymmetric Chern-Simons matter theories, unpublished.
J. Maldacena and A. Zhiboedov, Constraining conformal field theories with a slightly broken higher spin symmetry, Class. Quant. Grav.30 (2013) 104003 [arXiv:1204.3882] [INSPIRE].
G.J. Turiaci and A. Zhiboedov, Veneziano amplitude of Vasiliev theory, JHEP10 (2018) 034 [arXiv:1802.04390] [INSPIRE].
E.A. Ivanov, Chern-Simons matter systems with manifest N = 2 supersymmetry, Phys. Lett.B 268 (1991) 203 [INSPIRE].
J. Maldacena and A. Zhiboedov, Constraining conformal field theories with a higher spin symmetry, J. Phys.A 46 (2013) 214011 [arXiv:1112.1016] [INSPIRE].
L. Iliesiu et al., Fermion-scalar conformal blocks, JHEP04 (2016) 074 [arXiv:1511.01497] [INSPIRE].
A. Bedhotiya and S. Prakash, A test of bosonization at the level of four-point functions in Chern-Simons vector models, JHEP12 (2015) 032 [arXiv:1506.05412] [INSPIRE].
S. Caron-Huot, Analyticity in spin in conformal theories, JHEP09 (2017) 078 [arXiv:1703.00278] [INSPIRE].
D. Simmons-Duffin, D. Stanford and E. Witten, A spacetime derivation of the Lorentzian OPE inversion formula, JHEP07 (2018) 085 [arXiv:1711.03816] [INSPIRE].
O. Aharony, L.F. Alday, A. Bissi and R. Yacoby, The analytic bootstrap for large n Chern-Simons vector models, JHEP08 (2018) 166 [arXiv:1805.04377] [INSPIRE].
A.A. Nizami, T. Sharma and V. Umesh, Superspace formulation and correlation functions of 3d superconformal field theories, JHEP07 (2014) 022 [arXiv:1308.4778] [INSPIRE].
S.J. Gates, M.T. Grisaru, M. Roček and W. Siegel, Superspace or one thousand and one lessons in supersymmetry, Front. Phys.58 (1983) 1 [hep-th/0108200] [INSPIRE].
E. Witten, Supersymmetric index of three-dimensional gauge theory, hep-th/9903005 [INSPIRE].
E.I. Buchbinder, S.M. Kuzenko and I.B. Samsonov, Superconformal field theory in three dimensions: Correlation functions of conserved currents, JHEP06 (2015) 138 [arXiv:1503.04961] [INSPIRE].
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ArXiv ePrint: 1905.07146
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Aharony, O., Sharon, A. Large N renormalization group flows in 3d \( \mathcal{N} \) = 1 Chern-Simons-Matter theories. J. High Energ. Phys. 2019, 160 (2019). https://doi.org/10.1007/JHEP07(2019)160
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DOI: https://doi.org/10.1007/JHEP07(2019)160