Abstract
We study large N 2+1 dimensional fermions in the fundamental representation of an SU(N)k Chern Simons gauge group in the presence of a uniform background magnetic field for the U (1) global symmetry of this theory. The magnetic field modifies the Schwinger Dyson equation for the propagator in an interesting way; the product between the self energy and the Greens function is replaced by a Moyal star product. Employing a basis of functions previously used in the study of non-commutative solitons, we are able to exactly solve the Schwinger Dyson equation and so determine the fermion propagator. The propagator has a series of poles (and no other singularities) whose locations yield a spectrum of single particle energies at arbitrary t’ Hooft coupling and chemical potential. The usual free fermion Landau levels spectrum is shifted and broadened out; we compute the shifts and widths of these levels at arbitrary t’Hooft coupling. As a check on our results we independently solve for the propagators of the conjecturally dual theory of Chern Simons gauged large N fundamental Wilson Fisher bosons also in a background magnetic field but this time only at zero chemical potential. The spectrum of single particle states of the bosonic theory precisely agrees with those of the fermionic theory under Bose-Fermi duality.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
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].
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, 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].
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].
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].
O. Aharony, Baryons, monopoles and dualities in Chern-Simons-matter theories, JHEP 02 (2016) 093 [arXiv:1512.00161] [INSPIRE].
N. Seiberg, T. Senthil, C. Wang and E. Witten, A Duality Web in 2+1 Dimensions and Condensed Matter Physics, Annals Phys. 374 (2016) 395 [arXiv:1606.01989] [INSPIRE].
A. Karch and D. Tong, Particle-Vortex Duality from 3d Bosonization, Phys. Rev. X 6 (2016) 031043 [arXiv:1606.01893] [INSPIRE].
J. Murugan and H. Nastase, Particle-vortex duality in topological insulators and superconductors, JHEP 05 (2017) 159 [arXiv:1606.01912] [INSPIRE].
P.-S. Hsin and N. Seiberg, Level/rank Duality and Chern-Simons-Matter Theories, JHEP 09 (2016) 095 [arXiv:1607.07457] [INSPIRE].
O. Aharony, F. Benini, P.-S. Hsin and N. Seiberg, Chern-Simons-matter dualities with SO and U Sp gauge groups, JHEP 02 (2017) 072 [arXiv:1611.07874] [INSPIRE].
J. Gomis, Z. Komargodski and N. Seiberg, Phases Of Adjoint QCD3 And Dualities, SciPost Phys. 5 (2018) 007 [arXiv:1710.03258] [INSPIRE].
C. Córdova, P.-S. Hsin and N. Seiberg, Global Symmetries, Counterterms and Duality in Chern-Simons Matter Theories with Orthogonal Gauge Groups, SciPost Phys. 4 (2018) 021 [arXiv:1711.10008] [INSPIRE].
C. Córdova, P.-S. Hsin and N. Seiberg, Time-Reversal Symmetry, Anomalies and Dualities in (2+1)d, SciPost Phys. 5 (2018) 006 [arXiv:1712.08639] [INSPIRE].
M.A. Metlitski, A. Vishwanath and C. Xu, Duality and bosonization of (2+1)-dimensional Majorana fermions, Phys. Rev. B 95 (2017) 205137 [arXiv:1611.05049] [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].
S. Yokoyama, Scattering Amplitude and Bosonization Duality in General Chern-Simons Vector Models, JHEP 09 (2016) 105 [arXiv:1604.01897] [INSPIRE].
K. Inbasekar, S. Jain, P. Nayak and V. Umesh, All tree level scattering amplitudes in Chern-Simons theories with fundamental matter, Phys. Rev. Lett. 121 (2018) 161601 [arXiv:1710.04227] [INSPIRE].
K. Inbasekar et al., Dual superconformal symmetry of \( \mathcal{N} \) = 2 Chern-Simons theory with fundamental matter at large N , JHEP 06 (2019) 016 [arXiv:1711.02672] [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 S2 × S1 , JHEP 09 (2013) 009 [arXiv:1301.6169] [INSPIRE].
T. Takimi, Duality and higher temperature phases of large N Chern-Simons matter theories on S2 × S1 , 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. Jain, S. Minwalla and S. Yokoyama, Chern Simons duality with a fundamental boson and fermion, JHEP 11 (2013) 037 [arXiv:1305.7235] [INSPIRE].
S. Minwalla and S. Yokoyama, Chern Simons Bosonization along RG Flows, JHEP 02 (2016) 103 [arXiv:1507.04546] [INSPIRE].
G. Gur-Ari and R. Yacoby, Three Dimensional Bosonization From Supersymmetry, JHEP 11 (2015) 013 [arXiv:1507.04378] [INSPIRE].
M. Geracie, M. Goykhman and D.T. Son, Dense Chern-Simons Matter with Fermions at Large N , JHEP 04 (2016) 103 [arXiv:1511.04772] [INSPIRE].
D. Radičević, Disorder Operators in Chern-Simons-Fermion Theories, JHEP 03 (2016) 131 [arXiv:1511.01902] [INSPIRE].
S. Choudhury et al., Bose-Fermi Chern-Simons Dualities in the Higgsed Phase, JHEP 11 (2018) 177 [arXiv:1804.08635] [INSPIRE].
O. Aharony, S. Jain and S. Minwalla, Flows, Fixed Points and Duality in Chern-Simons-matter theories, JHEP 12 (2018) 058 [arXiv:1808.03317] [INSPIRE].
A. Dey, I. Halder, S. Jain, L. Janagal, S. Minwalla and N. Prabhakar, Duality and an exact Landau-Ginzburg potential for quasi-bosonic Chern-Simons-Matter theories, JHEP 11 (2018) 020 [arXiv:1808.04415] [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].
G.J. Turiaci and A. Zhiboedov, Veneziano Amplitude of Vasiliev Theory, JHEP 10 (2018) 034 [arXiv:1802.04390] [INSPIRE].
O. Aharony, L.F. Alday, A. Bissi and R. Yacoby, The Analytic Bootstrap for Large N Chern-Simons Vector Models, JHEP 08 (2018) 166 [arXiv:1805.04377] [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].
A. Kapustin, B. Willett and I. Yaakov, Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter, JHEP 03 (2010) 089 [arXiv:0909.4559] [INSPIRE].
N. Drukker, M. Marinõ and P. Putrov, Nonperturbative aspects of ABJM theory, JHEP 11 (2011) 141 [arXiv:1103.4844] [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].
R. Gopakumar, S. Minwalla and A. Strominger, Noncommutative solitons, JHEP 05 (2000) 020 [hep-th/0003160] [INSPIRE].
M. Aganagic, R. Gopakumar, S. Minwalla and A. Strominger, Unstable solitons in noncommutative gauge theory, JHEP 04 (2001) 001 [hep-th/0009142] [INSPIRE].
N. Seiberg and E. Witten, String theory and noncommutative geometry, JHEP 09 (1999) 032 [hep-th/9908142] [INSPIRE].
S. Minwalla, M. Van Raamsdonk and N. Seiberg, Noncommutative perturbative dynamics, JHEP 02 (2000) 020 [hep-th/9912072] [INSPIRE].
E. Witten, Quantum Field Theory and the Jones Polynomial, Commun. Math. Phys. 121 (1989) 351 [INSPIRE].
I. Halder, L. Janagal, S. Minwalla, N. Prabhakar, D. Radǐcević and T. Sharma, to appear.
S.-S. Lee, Low energy effective theory of Fermi surface coupled with U(1) gauge field in 2+1 dimensions, Phys. Rev. B 80 (2009) 165102 [arXiv:0905.4532] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1904.07885
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Halder, I., Minwalla, S. Matter Chern Simons theories in a background magnetic field. J. High Energ. Phys. 2019, 89 (2019). https://doi.org/10.1007/JHEP11(2019)089
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2019)089