Abstract
Using an explicit path integral approach we derive non-abelian bosonization and duality of 3D systems in the large N limit. We first consider a fermionic U(N) vector model coupled to level k Chern-Simons theory, following standard techniques we gauge the original global symmetry and impose the corresponding field strength F μν to vanish introducing a Lagrange multiplier Λ. Exchanging the order of integrations we obtain the bosonized theory with Λ as the propagating field using the large N rather than the previously used large mass limit. Next we follow the same procedure to dualize the scalar U (N) vector model coupled to Chern-Simons and find its corresponding dual theory. Finally, we compare the partition functions of the two resulting theories and find that they agree in the large N limit including a level/rank duality. This provides a constructive evidence for previous proposals on level/rank duality of 3D vector models in the large N limit. We also present a partial analysis at subleading order in large N and find that the duality does not generically hold at this level.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S.R. Coleman, The quantum sine-Gordon equation as the massive thirring model, Phys. Rev. D 11 (1975) 2088 [INSPIRE].
S. Mandelstam, Soliton operators for the quantized sine-Gordon equation, Phys. Rev. D 11 (1975) 3026 [INSPIRE].
E. Witten, Nonabelian bosonization in two-dimensions, Commun. Math. Phys. 92 (1984) 455.
C.P. Burgess and F. Quevedo, Bosonization as duality, Nucl. Phys. B 421 (1994) 373 [hep-th/9401105] [INSPIRE].
C.P. Burgess and F. Quevedo, Non-Abelian bosonization as duality, Phys. Lett. B 329 (1994) 457 [hep-th/9403173] [INSPIRE].
C.P. Burgess, C.A. Lütken and F. Quevedo, Bosonization in higher dimensions, Phys. Lett. B 336 (1994) 18 [hep-th/9407078] [INSPIRE].
E.H. Fradkin and F.A. Schaposnik, The Fermion-boson mapping in three-dimensional quantum field theory, Phys. Lett. B 338 (1994) 253 [hep-th/9407182] [INSPIRE].
S. Giombi and X. Yin, The higher spin/vector model duality, J. Phys. A 46 (2013) 214003 [arXiv:1208.4036] [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].
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].
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. 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].
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].
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. Minwalla and S. Yokoyama, Chern Simons duality with a fundamental boson and fermion, JHEP 11 (2013) 037 [arXiv:1305.7235] [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 and M. Moshe, Spontaneous breaking of scale invariance in a D = 3 U(N) model with Chern-Simons gauge fields, JHEP 06 (2014) 113 [arXiv:1402.4196] [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].
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].
E. Alvarez, L. Álvarez-Gaumé, J.L.F. Barbon and Y. Lozano, Some global aspects of duality in string theory, Nucl. Phys. B 415 (1994) 71 [hep-th/9309039] [INSPIRE].
E.F. Moreno and F.A. Schaposnik, Dualities and bosonization of massless fermions in three dimensional space-time, Phys. Rev. D 88 (2013) 025033 [arXiv:1303.6488] [INSPIRE].
A.N. Redlich, Gauge noninvariance and parity violation of three-dimensional fermions, Phys. Rev. Lett. 52 (1984) 18 [INSPIRE].
A.N. Redlich, Parity violation and gauge noninvariance of the effective gauge field action in three-dimensions, Phys. Rev. D 29 (1984) 2366 [INSPIRE].
A. Chan, T.L. Hughes, S. Ryu and E. Fradkin, Effective field theories for topological insulators by functional bosonization, Phys. Rev. B 87 (2013) 085132 [arXiv:1210.4305] [INSPIRE].
N. Bralic, E.H. Fradkin, V. Manias and F.A. Schaposnik, Bosonization of three-dimensional non-Abelian fermion field theories, Nucl. Phys. B 446 (1995) 144 [hep-th/9502066] [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].
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].
G.V. Dunne, Aspects of Chern-Simons theory, hep-th/9902115 [INSPIRE].
R. de Mello Koch, A. Jevicki, K. Jin and J.P. Rodrigues, AdS 4 /CF T 3 construction from collective fields, Phys. Rev. D 83 (2011) 025006 [arXiv:1008.0633] [INSPIRE].
M. Roček and E.P. Verlinde, Duality, quotients and currents, Nucl. Phys. B 373 (1992) 630 [hep-th/9110053] [INSPIRE].
V.P. Nair, The hamiltonian approach to Yang-Mills (2 + 1): an update and corrections to string tension, J. Phys. Conf. Ser. 462 (2013) 012039.
X.C. de la Ossa and F. Quevedo, Duality symmetries from non-Abelian isometries in string theory, Nucl. Phys. B 403 (1993) 377 [hep-th/9210021] [INSPIRE].
Y. Lozano, E. O Colgain, K. Sfetsos and D.C. Thompson, Non-abelian T-duality, ramond fields and coset geometries, JHEP 06 (2011) 106 [arXiv:1104.5196] [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1510.01335
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Muteeb, N., Zayas, L.A.P. & Quevedo, F. Dualities in 3D large N vector models. J. High Energ. Phys. 2016, 45 (2016). https://doi.org/10.1007/JHEP05(2016)045
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2016)045