Built on

W. Siegel, Supersymmetric Dimensional Regularization via Dimensional Reduction , Phys. Lett. 84B
1979
Earlier work this paper cites.
R. D. Pisarski, Fixed point structure of ϕ 6 \displaystyle\phi^{6} in three-dimensions at large N , Phys. Rev. Lett. 48
1982
Earlier work this paper cites.
A. N. Vasiliev, Yu. M. Pismak and Yu. R. Khonkonen, 1/N Expansion: Calculation of the exponent η \displaystyle\eta in the order 1 N 3 \displaystyle\frac{1}{N^{3}} by the conformal bootstrap method , Theor. Math. Phys. 50
1982
Earlier work this paper cites.
S. G. Naculich, H. A. Riggs and H. J. Schnitzer, Group Level Duality in WZW Models and Chern-Simons Theory , Phys. Lett. B246
1990
Earlier work this paper cites.
M. Camperi, F. Levstein and G. Zemba, The Large N \displaystyle N Limit of Chern-Simons Gauge Theory , Phys. Lett. B247
1990
Earlier work this paper cites.
T. Nakanishi and A. Tsuchiya, Level rank duality of WZW models in conformal field theory , Commun. Math. Phys. 144
1992
Earlier work this paper cites.
L. V. Avdeev, D. I. Kazakov and I. N. Kondrashuk, Renormalizations in supersymmetric and nonsupersymmetric nonAbelian Chern-Simons field theories with matter , Nucl. Phys. B391
1993
Earlier work this paper cites.
I. R. Klebanov and A. M. Polyakov, AdS dual of the critical O(N) vector model , Phys. Lett. B550
2002
Earlier work this paper cites.
E. Sezgin and P. Sundell, Massless higher spins and holography , Nucl. Phys. B644
2002
Earlier work this paper cites.
D. Gaiotto and X. Yin, Notes on superconformal Chern-Simons-Matter theories , JHEP 08
Original
2007
Earlier work this paper cites.
S. G. Naculich and H. J. Schnitzer, Level-rank duality of the U(N) WZW model, Chern-Simons theory, and 2-D qYM theory , JHEP 06
2007
Earlier work this paper cites.
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
Original
2008
Earlier work this paper cites.
A. Giveon and D. Kutasov, Seiberg Duality in Chern-Simons Theory , Nucl.Phys. B812
Original
2009
Earlier work this paper cites.
E. Pomoni and L. Rastelli, Large N Field Theory and AdS Tachyons , JHEP 04
Original
2009
Earlier work this paper cites.
S. Giombi and X. Yin, Higher Spin Gauge Theory and Holography: The Three-Point Functions , JHEP 09
Original
2010
Earlier work this paper cites.
F. Benini, C. Closset and S. Cremonesi, Comments on 3d Seiberg-like dualities , JHEP 1110
Original
2011
Earlier work this paper cites.
S. Giombi, S. Minwalla, S. Prakash, S. P. Trivedi, S. R. Wadia and X. Yin, Chern-Simons Theory with Vector Fermion Matter , Eur. Phys. J. C72
Original
2012
Earlier work this paper cites.
O. Aharony, G. Gur-Ari and R. Yacoby, d=3 Bosonic Vector Models Coupled to Chern-Simons Gauge Theories , JHEP 1203
Original
2012
Earlier work this paper cites.

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Later among the works it cites.
S. Jain, M. Mandlik, S. Minwalla, T. Takimi, S. R. Wadia and S. Yokoyama, Unitarity, Crossing Symmetry and Duality of the S-matrix in large N Chern-Simons theories with fundamental matter , JHEP 04
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Later among the works it cites.

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2018

Flows, Fixed Points and Duality in Chern-Simons-matter theories

Aharony, Ofer, Jain, Sachin, Minwalla, Shiraz

Understand

It has been conjectured that 3d fermions minimally coupled to Chern-Simons gauge fields are dual to 3d critical scalars, also minimally coupled to Chern-Simons gauge fields.

The large $N$ arguments for this duality can formally be used to show that Chern-Simons-gauged {\it critical} (Gross-Neveu) fermions are also dual to gauged `{\it regular}' scalars at every order in a $1/N$ expansion, provided both theories are well-defined (when one fine-tunes the two relevant parameters of each of these theories to zero).
In the strict large $N$ limit these `quasi-bosonic' theories appear as fixed lines parameterized by $x_6$, the coefficient of a sextic term in the potential.
While $x_6$ is an exactly marginal deformation at leading order in large $N$, it develops a non-trivial $\beta$ function at first subleading order in $1/N$.

Built on

W. Siegel, Supersymmetric Dimensional Regularization via Dimensional Reduction , Phys. Lett. 84B
1979
Earlier work this paper cites.
R. D. Pisarski, Fixed point structure of ϕ 6 \displaystyle\phi^{6} in three-dimensions at large N , Phys. Rev. Lett. 48
1982
Earlier work this paper cites.
A. N. Vasiliev, Yu. M. Pismak and Yu. R. Khonkonen, 1/N Expansion: Calculation of the exponent η \displaystyle\eta in the order 1 N 3 \displaystyle\frac{1}{N^{3}} by the conformal bootstrap method , Theor. Math. Phys. 50
1982
Earlier work this paper cites.
S. G. Naculich, H. A. Riggs and H. J. Schnitzer, Group Level Duality in WZW Models and Chern-Simons Theory , Phys. Lett. B246
1990
Earlier work this paper cites.
M. Camperi, F. Levstein and G. Zemba, The Large N \displaystyle N Limit of Chern-Simons Gauge Theory , Phys. Lett. B247
1990
Earlier work this paper cites.
T. Nakanishi and A. Tsuchiya, Level rank duality of WZW models in conformal field theory , Commun. Math. Phys. 144
1992
Earlier work this paper cites.
L. V. Avdeev, D. I. Kazakov and I. N. Kondrashuk, Renormalizations in supersymmetric and nonsupersymmetric nonAbelian Chern-Simons field theories with matter , Nucl. Phys. B391
1993
Earlier work this paper cites.
I. R. Klebanov and A. M. Polyakov, AdS dual of the critical O(N) vector model , Phys. Lett. B550
2002
Earlier work this paper cites.
E. Sezgin and P. Sundell, Massless higher spins and holography , Nucl. Phys. B644
2002
Earlier work this paper cites.
D. Gaiotto and X. Yin, Notes on superconformal Chern-Simons-Matter theories , JHEP 08
Original
2007
Earlier work this paper cites.
S. G. Naculich and H. J. Schnitzer, Level-rank duality of the U(N) WZW model, Chern-Simons theory, and 2-D qYM theory , JHEP 06
2007
Earlier work this paper cites.
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
Original
2008
Earlier work this paper cites.
A. Giveon and D. Kutasov, Seiberg Duality in Chern-Simons Theory , Nucl.Phys. B812
Original
2009
Earlier work this paper cites.
E. Pomoni and L. Rastelli, Large N Field Theory and AdS Tachyons , JHEP 04
Original
2009
Earlier work this paper cites.
S. Giombi and X. Yin, Higher Spin Gauge Theory and Holography: The Three-Point Functions , JHEP 09
Original
2010
Earlier work this paper cites.
F. Benini, C. Closset and S. Cremonesi, Comments on 3d Seiberg-like dualities , JHEP 1110
Original
2011
Earlier work this paper cites.
S. Giombi, S. Minwalla, S. Prakash, S. P. Trivedi, S. R. Wadia and X. Yin, Chern-Simons Theory with Vector Fermion Matter , Eur. Phys. J. C72
Original
2012
Earlier work this paper cites.
O. Aharony, G. Gur-Ari and R. Yacoby, d=3 Bosonic Vector Models Coupled to Chern-Simons Gauge Theories , JHEP 1203
Original
2012
Earlier work this paper cites.