Abstract
It has previously been conjectured that the theory of free fundamental scalars minimally coupled to a Chern Simons gauge field is dual to the theory of critical fundamental fermions minimally coupled to a level rank dual Chern Simons gauge field. In this paper we study RG flows away from these two fixed points by turning on relevant operators. In the ’t Hooft large N limit we compute the thermal partition along each of these flows and find a map of parameters under which the two partition functions agree exactly with each other all the way from the UV to the IR. We conjecture that the bosonic and fermionic RG flows are dual to each other under this map of parameters. Our flows can be tuned to end at the gauged critical scalar theory and gauged free fermionic theories respectively. Assuming the validity of our conjecture, this tuned trajectory may be viewed as RG flow from the gauged theory of free bosons to the gauged theory of free fermions.
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References
K.G. Wilson and M.E. Fisher, Critical exponents in 3.99 dimensions, Phys. Rev. Lett. 28 (1972) 240 [INSPIRE].
B. Rosenstein, B.J. Warr and S.H. Park, The Four Fermi Theory Is Renormalizable in (2+1)-Dimensions, Phys. Rev. Lett. 62 (1989) 1433 [INSPIRE].
I. Ya. Arefeva and S.I. Azakov, Renormalization and phase transition in the quantum CP N −1 model (D = 2, 3), Nucl. Phys. B 162 (1980) 298 [INSPIRE].
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. 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].
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].
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].
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].
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].
W.A. Bardeen, The Massive Fermion Phase for the U(N) Chern-Simons Gauge Theory in D = 3 at Large-N, JHEP 10 (2014) 39 [arXiv:1404.7477] [INSPIRE].
V. Gurucharan and S. Prakash, Anomalous dimensions in non-supersymmetric bifundamental Chern-Simons theories, JHEP 09 (2014) 009 [arXiv:1404.7849] [INSPIRE].
Y. Frishman and J. Sonnenschein, Large-N Chern-Simons with massive fundamental fermions - A model with no bound states, JHEP 12 (2014) 165 [arXiv:1409.6083] [INSPIRE].
M. Moshe and J. Zinn-Justin, 3D Field Theories with Chern-Simons Term for Large-N in the Weyl Gauge, JHEP 01 (2015) 054 [arXiv:1410.0558] [INSPIRE].
A. Bedhotiya and S. Prakash, A test of bosonization at the level of four-point functions in Chern-Simons vector models, JHEP 12 (2015) 032 [arXiv:1506.05412] [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].
S. Yokoyama, Chern-Simons-Fermion Vector Model with Chemical Potential, JHEP 01 (2013) 052 [arXiv:1210.4109] [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].
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].
S. Jain, S. Minwalla and S. Yokoyama, Chern Simons duality with a fundamental boson and fermion, JHEP 11 (2013) 037 [arXiv:1305.7235] [INSPIRE].
T. Takimi, Duality and higher temperature phases of large-N Chern-Simons matter theories on S 2 × S 1, JHEP 07 (2013) 177 [arXiv:1304.3725] [INSPIRE].
S. Yokoyama, A Note on Large-N Thermal Free Energy in Supersymmetric Chern-Simons Vector Models, JHEP 01 (2014) 148 [arXiv:1310.0902] [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].
S. Banerjee and D. Radičevič, Chern-Simons theory coupled to bifundamental scalars, JHEP 06 (2014) 168 [arXiv:1308.2077] [INSPIRE].
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 (2015) 129 [arXiv:1404.6373] [INSPIRE].
Y. Dandekar, M. Mandlik and S. Minwalla, Poles in the S-Matrix of Relativistic Chern-Simons Matter theories from Quantum Mechanics, JHEP 04 (2015) 102 [arXiv:1407.1322] [INSPIRE].
K. Inbasekar, S. Jain, S. Mazumdar, S. Minwalla, V. Umesh and S. Yokoyama, Unitarity, crossing symmetry and duality in the scattering of \( \mathcal{N}=1 \) SUSY matter Chern-Simons theories, JHEP 10 (2015) 176 [arXiv:1505.06571] [INSPIRE].
G. Gur-Ari and R. Yacoby, Three Dimensional Bosonization From Supersymmetry, JHEP 11 (2015) 013 [arXiv:1507.04378] [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].
E. Witten, Multitrace operators, boundary conditions and AdS/CFT correspondence, hep-th/0112258 [INSPIRE].
M. Berkooz, A. Sever and A. Shomer, ‘Double trace’ deformations, boundary conditions and space-time singularities, JHEP 05 (2002) 034 [hep-th/0112264] [INSPIRE].
I.R. Klebanov and A.M. Polyakov, AdS dual of the critical O(N) vector model, Phys. Lett. B 550 (2002) 213 [hep-th/0210114] [INSPIRE].
I.R. Klebanov and E. Witten, AdS/CFT correspondence and symmetry breaking, Nucl. Phys. B 556 (1999) 89 [hep-th/9905104] [INSPIRE].
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Minwalla, S., Yokoyama, S. Chern Simons bosonization along RG flows. J. High Energ. Phys. 2016, 103 (2016). https://doi.org/10.1007/JHEP02(2016)103
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DOI: https://doi.org/10.1007/JHEP02(2016)103