Abstract
We consider Quantum Electrodynamics in 2 + 1 dimensions with Nf fermionic or bosonic flavors, allowing for interactions that respect the global symmetry U(Nf/2)2. There are four bosonic and four fermionic fixed points, which we analyze using the large Nf expansion. We systematically compute, at order O(1/Nf), the scaling dimensions of quadratic and quartic mesonic operators.
We also consider Quantum Electrodynamics with minimal supersymmetry. In this case the large Nf scaling dimensions, extrapolated at Nf = 2, agree quite well with the scaling dimensions of a dual supersymmetric Gross-Neveu-Yukawa model. This provides a quantitative check of the conjectured duality.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Benvenuti and H. Khachatryan, QED’s in 2 + 1 dimensions: complex fixed points and dualities, arXiv:1812.01544 [INSPIRE].
T. Senthil, Deconfined quantum critical points, Science 303 (2004) 1490 [INSPIRE].
T. Senthil, L. Balents, S. Sachdev, A. Vishwanath and M.P.A. Fisher, Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm, Phys. Rev. B 70 (2004) 144407 [cond-mat/0312617].
O.I. Motrunich and A. Vishwanath, Emergent photons and new transitions in the O(3) σ-model with hedgehog suppression, Phys. Rev. B 70 (2004) 075104 [cond-mat/0311222] [INSPIRE].
V. Gorbenko, S. Rychkov and B. Zan, Walking, weak first-order transitions and complex CFTs, JHEP 10 (2018) 108 [arXiv:1807.11512] [INSPIRE].
K.-I. Kubota and H. Terao, Dynamical symmetry breaking in QED 3 from the Wilson RG point of view, Prog. Theor. Phys. 105 (2001) 809 [hep-ph/0101073] [INSPIRE].
K. Kaveh and I.F. Herbut, Chiral symmetry breaking in QED 3 in presence of irrelevant interactions: a renormalization group study, Phys. Rev. B 71 (2005) 184519 [cond-mat/0411594] [INSPIRE].
I.F. Herbut, Chiral symmetry breaking in three-dimensional quantum electrodynamics as fixed point annihilation, Phys. Rev. D 94 (2016) 025036 [arXiv:1605.09482] [INSPIRE].
V.P. Gusynin and P.K. Pyatkovskiy, Critical number of fermions in three-dimensional QED, Phys. Rev. D 94 (2016) 125009 [arXiv:1607.08582] [INSPIRE].
A.V. Kotikov and S. Teber, Addendum to “critical behaviour of (2 + 1)-dimensional QED: 1/N f -corrections in an arbitrary non-local gauge”, Phys. Rev. D 99 (2019) 059902 [arXiv:1902.03790] [INSPIRE].
S. Giombi, I.R. Klebanov and G. Tarnopolsky, Conformal QED d , F-theorem and the ϵ expansion, J. Phys. A 49 (2016) 135403 [arXiv:1508.06354] [INSPIRE].
R.D. Pisarski, Chiral symmetry breaking in three-dimensional electrodynamics, Phys. Rev. D 29 (1984) 2423 [INSPIRE].
L. Di Pietro, Z. Komargodski, I. Shamir and E. Stamou, Quantum electrodynamics in d = 3 from the ϵ expansion, Phys. Rev. Lett. 116 (2016) 131601 [arXiv:1508.06278] [INSPIRE].
L. Di Pietro and E. Stamou, Scaling dimensions in QED 3 from the ϵ-expansion, JHEP 12 (2017) 054 [arXiv:1708.03740] [INSPIRE].
Z. Li, Solving QED 3 with conformal bootstrap, arXiv:1812.09281 [INSPIRE].
J. March-Russell, On the possibility of second order phase transitions in spontaneously broken gauge theories, Phys. Lett. B 296 (1992) 364 [hep-ph/9208215] [INSPIRE].
A. Nahum, J.T. Chalker, P. Serna, M. Ortuño and A.M. Somoza, Deconfined quantum criticality, scaling violations and classical loop models, Phys. Rev. X 5 (2015) 041048 [arXiv:1506.06798] [INSPIRE].
A. Nahum, P. Serna, J.T. Chalker, M. Ortuño and A.M. Somoza, Emergent SO(5) symmetry at the Néel to valence-bond-solid transition, Phys. Rev. Lett. 115 (2015) 267203 [arXiv:1508.06668] [INSPIRE].
P. Serna and A. Nahum, Emergence and spontaneous breaking of approximate O(4) symmetry at a weakly first-order deconfined phase transition, Phys. Rev. B 99 (2019) 195110 [arXiv:1805.03759] [INSPIRE].
F.S. Nogueira and A. Sudbø, Deconfined quantum criticality and conformal phase transition in two-dimensional antiferromagnets, EPL 104 (2013) 56004 [arXiv:1304.4938] [INSPIRE].
A. Karch and D. Tong, Particle-vortex duality from 3d bosonization, Phys. Rev. X 6 (2016) 031043 [arXiv:1606.01893] [INSPIRE].
C. Wang, A. Nahum, M.A. Metlitski, C. Xu and T. Senthil, Deconfined quantum critical points: symmetries and dualities, Phys. Rev. X 7 (2017) 031051 [arXiv:1703.02426] [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. 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, Correlation functions of large N Chern-Simons-matter theories and bosonization in three dimensions, JHEP 12 (2012) 028 [arXiv:1207.4593] [INSPIRE].
D.T. Son, Is the composite fermion a Dirac particle?, Phys. Rev. X 5 (2015) 031027 [arXiv:1502.03446] [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, B. Robinson and D. Tong, More Abelian dualities in 2 + 1 dimensions, JHEP 01 (2017) 017 [arXiv:1609.04012] [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].
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 USp gauge groups, JHEP 02 (2017) 072 [arXiv:1611.07874] [INSPIRE].
F. Benini, P.-S. Hsin and N. Seiberg, Comments on global symmetries, anomalies and duality in (2 + 1)d, JHEP 04 (2017) 135 [arXiv:1702.07035] [INSPIRE].
F. Benini, Three-dimensional dualities with bosons and fermions, JHEP 02 (2018) 068 [arXiv:1712.00020] [INSPIRE].
K. Jensen, A master bosonization duality, JHEP 01 (2018) 031 [arXiv:1712.04933] [INSPIRE].
Z. Komargodski and N. Seiberg, A symmetry breaking scenario for QCD 3, JHEP 01 (2018) 109 [arXiv:1706.08755] [INSPIRE].
J. Gomis, Z. Komargodski and N. Seiberg, Phases of adjoint QCD 3 and dualities, SciPost Phys. 5 (2018) 007 [arXiv:1710.03258] [INSPIRE].
V. Bashmakov, J. Gomis, Z. Komargodski and A. Sharon, Phases of N = 1 theories in 2 + 1 dimensions, JHEP 07 (2018) 123 [arXiv:1802.10130] [INSPIRE].
F. Benini and S. Benvenuti, N = 1 dualities in 2 + 1 dimensions, JHEP 11 (2018) 197 [arXiv:1803.01784] [INSPIRE].
C. Choi, M. Roček and A. Sharon, Dualities and phases of 3D N = 1 SQCD, JHEP 10 (2018) 105 [arXiv:1808.02184] [INSPIRE].
C. Choi, D. Delmastro, J. Gomis and Z. Komargodski, Dynamics of QCD 3 with rank-two quarks and duality, arXiv:1810.07720 [INSPIRE].
T. Senthil, D.T. Son, C. Wang and C. Xu, Duality between (2 + 1)d quantum critical points, arXiv:1810.05174 [INSPIRE].
J. Lou, A.W. Sandvik and N. Kawashima, Antiferromagnetic to valence-bond-soild transitions in two-dimensional SU(N) Heisenberg models with multi-spin interactions, Phys. Rev. B 80 (2009) 180414 [arXiv:0908.0740].
R.K. Kaul and A.W. Sandvik, Lattice model for the SU(N) Néel to valence-bond solid quantum phase transition at large N, Phys. Rev. Lett. 108 (2012) 137201 [arXiv:1110.4130] [INSPIRE].
J. D’Emidio and R.K. Kaul, New easy-plane CP N − 1 fixed points, Phys. Rev. Lett. 118 (2017) 187202 [arXiv:1610.07702] [INSPIRE].
X.-F. Zhang, Y.-C. He, S. Eggert, R. Moessner and F. Pollmann, Continuous easy-plane deconfined phase transition on the Kagome lattice, Phys. Rev. Lett. 120 (2018) 115702 [arXiv:1706.05414] [INSPIRE].
N. Karthik and R. Narayanan, Scale-invariance of parity-invariant three-dimensional QED, Phys. Rev. D 94 (2016) 065026 [arXiv:1606.04109] [INSPIRE].
Y. Nakayama and T. Ohtsuki, Conformal bootstrap dashing hopes of emergent symmetry, Phys. Rev. Lett. 117 (2016) 131601 [arXiv:1602.07295] [INSPIRE].
D. Simmons-Duffin, unpublished.
L. Iliesiu, The Néel-VBA quantum phase transition and the conformal bootstrap, talk at Simons Center for Geometry and Physics, 5 November 2018.
D. Poland, S. Rychkov and A. Vichi, The conformal bootstrap: theory, numerical techniques and applications, Rev. Mod. Phys. 91 (2019) 15002 [arXiv:1805.04405] [INSPIRE].
I.R. Klebanov, S.S. Pufu, S. Sachdev and B.R. Safdi, Entanglement entropy of 3D conformal gauge theories with many flavors, JHEP 05 (2012) 036 [arXiv:1112.5342] [INSPIRE].
S.S. Pufu, Anomalous dimensions of monopole operators in three-dimensional quantum electrodynamics, Phys. Rev. D 89 (2014) 065016 [arXiv:1303.6125] [INSPIRE].
E. Dyer, M. Mezei, S.S. Pufu and S. Sachdev, Scaling dimensions of monopole operators in the \( C{P^{N_b-}}^1 \) theory in 2 + 1 dimensions, JHEP 06 (2015) 037 [Erratum ibid. 03 (2016) 111] [arXiv:1504.00368] [INSPIRE].
K. Diab, L. Fei, S. Giombi, I.R. Klebanov and G. Tarnopolsky, On C J and C T in the Gross-Neveu and O(N) models, J. Phys. A 49 (2016) 405402 [arXiv:1601.07198] [INSPIRE].
S. Giombi, G. Tarnopolsky and I.R. Klebanov, On C J and C T in conformal QED, JHEP 08 (2016) 156 [arXiv:1602.01076] [INSPIRE].
S.M. Chester, L.V. Iliesiu, M. Mezei and S.S. Pufu, Monopole operators in U(1) Chern-Simons-matter theories, JHEP 05 (2018) 157 [arXiv:1710.00654] [INSPIRE].
G. Murthy and S. Sachdev, Action of hedgehog instantons in the disordered phase of the (2 + 1)-dimensional CP N − 1 model, Nucl. Phys. B 344 (1990) 557 [INSPIRE].
V. Borokhov, A. Kapustin and X.-K. Wu, Topological disorder operators in three-dimensional conformal field theory, JHEP 11 (2002) 049 [hep-th/0206054] [INSPIRE].
S. Giombi and V. Kirilin, Anomalous dimensions in CFT with weakly broken higher spin symmetry, JHEP 11 (2016) 068 [arXiv:1601.01310] [INSPIRE].
A.N. Manashov and E.D. Skvortsov, Higher-spin currents in the Gross-Neveu model at 1/N 2, JHEP 01 (2017) 132 [arXiv:1610.06938] [INSPIRE].
A.N. Manashov, E.D. Skvortsov and M. Strohmaier, Higher spin currents in the critical O(N) vector model at 1/N 2, JHEP 08 (2017) 106 [arXiv:1706.09256] [INSPIRE].
A.N. Manashov and M. Strohmaier, Correction exponents in the Gross-Neveu-Yukawa model at 1/N 2, Eur. Phys. J. C 78 (2018) 454 [arXiv:1711.02493] [INSPIRE].
J.A. Gracey, Large N f quantum field theory, Int. J. Mod. Phys. A 33 (2019) 1830032 [arXiv:1812.05368] [INSPIRE].
D. Gaiotto, Z. Komargodski and J. Wu, Curious aspects of three-dimensional N = 1 SCFTs, JHEP 08 (2018) 004 [arXiv:1804.02018] [INSPIRE].
F. Benini and S. Benvenuti, N = 1 QED in 2 + 1 dimensions: dualities and enhanced symmetries, arXiv:1804.05707 [INSPIRE].
P. Calabrese, A. Pelissetto and E. Vicari, Multicritical phenomena in O(n 1) + O(n 2) symmetric theories, Phys. Rev. B 67 (2003) 054505 [cond-mat/0209580] [INSPIRE].
B.i. Halperin, T.C. Lubensky and S.-K. Ma, First order phase transitions in superconductors and smectic A liquid crystals, Phys. Rev. Lett. 32 (1974) 292 [INSPIRE].
S. Hikami, Renormalization group functions of CP N − 1 nonlinear σ-model and N component scalar QED model, Prog. Theor. Phys. 62 (1979) 226 [INSPIRE].
A.N. Vasiliev and M. Yu. Nalimov, The CP N − 1 model: calculation of anomalous dimensions and the mixing matrices in the order 1/N, Theor. Math. Phys. 56 (1983) 643 [Teor. Mat. Fiz. 56 (1983) 15] [INSPIRE].
R.K. Kaul and S. Sachdev, Quantum criticality of U(1) gauge theories with fermionic and bosonic matter in two spatial dimensions, Phys. Rev. B 77 (2008) 155105 [arXiv:0801.0723] [INSPIRE].
J. Braun, H. Gies, L. Janssen and D. Roscher, Phase structure of many-flavor QED 3, Phys. Rev. D 90 (2014) 036002 [arXiv:1404.1362] [INSPIRE].
L. Janssen and Y.-C. He, Critical behavior of the QED 3 -Gross-Neveu model: duality and deconfined criticality, Phys. Rev. B 96 (2017) 205113 [arXiv:1708.02256] [INSPIRE].
B. Ihrig, L. Janssen, L.N. Mihaila and M.M. Scherer, Deconfined criticality from the QED 3 -Gross-Neveu model at three loops, Phys. Rev. B 98 (2018) 115163 [arXiv:1807.04958] [INSPIRE].
N. Zerf, P. Marquard, R. Boyack and J. Maciejko, Critical behavior of the QED 3 -Gross-Neveu-Yukawa model at four loops, Phys. Rev. B 98 (2018) 165125 [arXiv:1808.00549] [INSPIRE].
C. Xu, Renormalization group studies on four-fermion interaction instabilities on algebraic spin liquids, Phys. Rev. B 78 (2008) 054432 [arXiv:0803.0794].
S.M. Chester and S.S. Pufu, Anomalous dimensions of scalar operators in QED 3, JHEP 08 (2016) 069 [arXiv:1603.05582] [INSPIRE].
W. Rantner and X.-G. Wen, Spin correlations in the algebraic spin liquid: implications for high-T c superconductors, Phys. Rev. B 66 (2002) 144501 [cond-mat/0201521] [INSPIRE].
M. Hermele, T. Senthil and M.P.A. Fisher, Algebraic spin liquid as the mother of many competing orders, Phys. Rev. B 72 (2005) 104404 [Erratum ibid. B 76 (2007) 149906] [cond-mat/0502215] [INSPIRE].
R. Boyack, A. Rayyan and J. Maciejko, Deconfined criticality in the QED 3 -Gross-Neveu-Yukawa model: the 1/N expansion revisited, Phys. Rev. B 99 (2019) 195135 [arXiv:1812.02720] [INSPIRE].
J.A. Gracey, Gauged Nambu-Jona-Lasinio model at O(1/N) with and without a Chern-Simons term, Mod. Phys. Lett. A 8 (1993) 2205 [hep-th/9306105] [INSPIRE].
J.A. Gracey, Critical point analysis of various fermionic field theories in the large N expansion, J. Phys. A 25 (1992) L109 [INSPIRE].
J.A. Gracey, Gauge independent critical exponents for QED coupled to a four Fermi interaction with and without a Chern-Simons term, Annals Phys. 224 (1993) 275 [hep-th/9301113] [INSPIRE].
J.A. Gracey, Fermion bilinear operator critical exponents at O(1/N 2) in the QED-Gross-Neveu universality class, Phys. Rev. D 98 (2018) 085012 [arXiv:1808.07697] [INSPIRE].
S.J. Gates, M.T. Grisaru, M. Roček and W. Siegel, Superspace or one thousand and one lessons in supersymmetry, Front. Phys. 58 (1983) 1 [hep-th/0108200] [INSPIRE].
K.A. Intriligator and N. Seiberg, Mirror symmetry in three-dimensional gauge theories, Phys. Lett. B 387 (1996) 513 [hep-th/9607207] [INSPIRE].
A. Kapustin and M.J. Strassler, On mirror symmetry in three-dimensional Abelian gauge theories, JHEP 04 (1999) 021 [hep-th/9902033] [INSPIRE].
M. Gremm and E. Katz, Mirror symmetry for N = 1 QED in three-dimensions, JHEP 02 (2000) 008 [hep-th/9906020] [INSPIRE].
J.A. Gracey, Critical exponents for the supersymmetric σ model, J. Phys. A 23 (1990) 2183 [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: 1902.05767
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, 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 licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Benvenuti, S., Khachatryan, H. Easy-plane QED3’s in the large Nf limit. J. High Energ. Phys. 2019, 214 (2019). https://doi.org/10.1007/JHEP05(2019)214
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2019)214