Abstract
We compute the exact effective action for \( \mathcal{N} \) = 3 U(N) k and \( \mathcal{N} \) = 4, 6 U(N) k × U(N′)−k Chern-Simons theories with minimal matter content in the ’t Hooft vector model limit under which N and k go to infinity holding N/k,N′ fixed. We also extend this calculation to \( \mathcal{N} \) = 4, 6 mass deformed case. We show that those large N effective actions except mass-deformed \( \mathcal{N} \) = 6 case precisely reduce to that of \( \mathcal{N} \) = 2 U(N) k Chern-Simons theory with one fundamental chiral field up to overall multiple factor. By using this result we argue the thermal free energy and self-duality of the \( \mathcal{N} \) = 3, 4, 6 Chern-Simons theories including the \( \mathcal{N} \) = 4 mass term reduce to those of the \( \mathcal{N} \) = 2 case under the limit.
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References
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, JHEP 03 (2012) 037 [arXiv:1110.4382] [INSPIRE].
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].
S. Giombi, S. Prakash and X. Yin, A Note on CFT Correlators in Three Dimensions, JHEP 07 (2013) 105 [arXiv:1104.4317] [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].
O. Aharony, G. Gur-Ari and R. Yacoby, Correlation Functions of Large N Chern-Simons-Matter Theories and Bosonization in Three Dimensions, JHEP 12 (2012) 028 [arXiv:1207.4593] [INSPIRE].
G. Gur-Ari and R. Yacoby, Correlators of Large N Fermionic Chern-Simons Vector Models, JHEP 02 (2013) 150 [arXiv:1211.1866] [INSPIRE].
S. Jain, S.P. Trivedi, S.R. Wadia and S. Yokoyama, Supersymmetric Chern-Simons Theories with Vector Matter, JHEP 10 (2012) 194 [arXiv:1207.4750] [INSPIRE].
O. Aharony, G. Gur-Ari and R. Yacoby, unpublished.
S. Yokoyama, Chern-Simons-Fermion Vector Model with Chemical Potential, JHEP 01 (2013) 052 [arXiv:1210.4109] [INSPIRE].
S.H. Shenker and X. Yin, Vector Models in the Singlet Sector at Finite Temperature, arXiv:1109.3519 [INSPIRE].
S. Banerjee, S. Hellerman, J. Maltz and S.H. Shenker, Light States in Chern-Simons Theory Coupled to Fundamental Matter, JHEP 03 (2013) 097 [arXiv:1207.4195] [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, S. Giombi, G. Gur-Ari, J. Maldacena and R. Yacoby, The Thermal Free Energy in Large N Chern-Simons-Matter Theories, JHEP 03 (2013) 121 [arXiv:1211.4843] [INSPIRE].
M.R. Douglas, Chern-Simons-Witten theory as a topological Fermi liquid, hep-th/9403119 [INSPIRE].
S. Jain, S. Minwalla, T. Sharma, T. Takimi, S.R. Wadia and S. Yokoyama, Phases of large-N vector Chern-Simons theories on S 2 × S 1, JHEP 09 (2013) 009 [arXiv:1301.6169] [INSPIRE].
T. Takimi, Duality and Higher Temperature Phases of Large-N Chern-Simons Matter Theories on S 2 × S 1, arXiv:1304.3725 [INSPIRE].
S. Jain, S. Minwalla and S. Yokoyama, Chern Simons duality with a fundamental boson and fermion, JHEP 11 (2013) 037 [arXiv:1305.7235] [INSPIRE].
J.H. Schwarz, Superconformal Chern-Simons theories, JHEP 11 (2004) 078 [hep-th/0411077] [INSPIRE].
D. Gaiotto and E. Witten, Janus Configurations, Chern-Simons Couplings, And The theta-Angle in N = 4 Super Yang-Mills Theory, JHEP 06 (2010) 097 [arXiv:0804.2907] [INSPIRE].
D. Gaiotto and X. Yin, Notes on superconformal Chern-Simons-Matter theories, JHEP 08 (2007) 056 [arXiv:0704.3740] [INSPIRE].
K. Hosomichi, K.-M. Lee, S. Lee, S. Lee and J. Park, N = 4 Superconformal Chern-Simons Theories with Hyper and Twisted Hyper Multiplets, JHEP 07 (2008) 091 [arXiv:0805.3662] [INSPIRE].
M. Benna, I. Klebanov, T. Klose and M. Smedback, Superconformal Chern-Simons Theories and AdS 4 /CF T 3 Correspondence, JHEP 09 (2008) 072 [arXiv:0806.1519] [INSPIRE].
J. Gomis, D. Rodriguez-Gomez, M. Van Raamsdonk and H. Verlinde, A Massive Study of M2-brane Proposals, JHEP 09 (2008) 113 [arXiv:0807.1074] [INSPIRE].
O. Aharony, O. Bergman and D.L. Jafferis, Fractional M2-branes, JHEP 11 (2008) 043 [arXiv:0807.4924] [INSPIRE].
L.N. Cooper, Bound electron pairs in a degenerate Fermi gas, Phys. Rev. 104 (1956) 1189 [INSPIRE].
S. Banerjee and D. Radicevic, Chern-Simons theory coupled to bifundamental scalars, arXiv:1308.2077 [INSPIRE].
Y. Frishman and J. Sonnenschein, Breaking conformal invariance - Large N Chern-Simons theory coupled to massive fundamental fermions, JHEP 12 (2013) 091 [arXiv:1306.6465] [INSPIRE].
A.A. Nizami, T. Sharma and V. Umesh, Superspace formulation and correlation functions of 3d superconformal field theories, arXiv:1308.4778 [INSPIRE].
M.A. Vasiliev, Consistent equation for interacting gauge fields of all spins in (3 + 1)-dimensions, Phys. Lett. B 243 (1990) 378 [INSPIRE].
C.-M. Chang, S. Minwalla, T. Sharma and X. Yin, ABJ Triality: from Higher Spin Fields to Strings, J. Phys. A 46 (2013) 214009 [arXiv:1207.4485] [INSPIRE].
I. Klebanov and A. Polyakov, AdS dual of the critical O(N) vector model, Phys. Lett. B 550 (2002) 213 [hep-th/0210114] [INSPIRE].
E. Sezgin and P. Sundell, Massless higher spins and holography, Nucl. Phys. B 644 (2002) 303 [Erratum ibid. B 660 (2003) 403] [hep-th/0205131] [INSPIRE].
E. Sezgin and P. Sundell, Holography in 4D (super) higher spin theories and a test via cubic scalar couplings, JHEP 07 (2005) 044 [hep-th/0305040] [INSPIRE].
S. Giombi and X. Yin, Higher Spin Gauge Theory and Holography: The Three-Point Functions, JHEP 09 (2010) 115 [arXiv:0912.3462] [INSPIRE].
S. Giombi and X. Yin, Higher Spins in AdS and Twistorial Holography, JHEP 04 (2011) 086 [arXiv:1004.3736] [INSPIRE].
S. Giombi and X. Yin, On Higher Spin Gauge Theory and the Critical O(N) Model, Phys. Rev. D 85 (2012) 086005 [arXiv:1105.4011] [INSPIRE].
S. Giombi and X. Yin, The Higher Spin/Vector Model Duality, J. Phys. A 46 (2013) 214003 [arXiv:1208.4036] [INSPIRE].
E. Sezgin and P. Sundell, Supersymmetric Higher Spin Theories, J. Phys. A 46 (2013) 214022 [arXiv:1208.6019] [INSPIRE].
S. Giombi, I.R. Klebanov, S.S. Pufu, B.R. Safdi and G. Tarnopolsky, AdS Description of Induced Higher-Spin Gauge Theory, JHEP 10 (2013) 016 [arXiv:1306.5242] [INSPIRE].
S. Giombi and I.R. Klebanov, One Loop Tests of Higher Spin AdS/CFT, JHEP 12 (2013) 068 [arXiv:1308.2337] [INSPIRE].
A. Tseytlin, On partition function and Weyl anomaly of conformal higher spin fields, Nucl. Phys. B 877 (2013) 598 [arXiv:1309.0785] [INSPIRE].
O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].
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Yokoyama, S. A note on large N thermal free energy in supersymmetric Chern-Simons vector models. J. High Energ. Phys. 2014, 148 (2014). https://doi.org/10.1007/JHEP01(2014)148
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DOI: https://doi.org/10.1007/JHEP01(2014)148