Abstract
We study the fate of weakly coupled dual QED3 in the infrared, that is, a single two-component Dirac fermion coupled to an emergent U(1) gauge field, but without Chern-Simons term. This theory has recently been proposed as a dual description of 2D surfaces of certain topological insulators. Using the renormalization group, we find that the interplay of gauge fluctuations with generated interactions in the four-fermi sector stabilizes an interacting conformal field theory (CFT) with finite four-fermi coupling in the infrared. The emergence of this CFT is due to cancellations in the β-function of the four-fermi coupling special to “N F = 1/2”. We also quantify how a possible “strong” Dirac fermion duality between a free Dirac cone and dual QED3 would constrain the universal constants of the topological current correlator of the latter.
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References
D.T. Son, Is the composite fermion a Dirac particle?, Phys. Rev. X 5 (2015) 031027 [arXiv:1502.03446] [INSPIRE].
M.A. Metlitski and A. Vishwanath, Particle-vortex duality of two-dimensional Dirac fermion from electric-magnetic duality of three-dimensional topological insulators, Phys. Rev. B 93 (2016) 245151 [arXiv:1505.05142] [INSPIRE].
C. Wang and T. Senthil, Dual dirac liquid on the surface of the electron topological insulator, Phys. Rev. X 5 (2015) 041031 [arXiv:1505.05141] [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].
C. Vafa and E. Witten, Eigenvalue inequalities for fermions in gauge theories, Commun. Math. Phys. 95 (1984) 257 [INSPIRE].
D.F. Mross, J. Alicea and O.I. Motrunich, Explicit derivation of duality between a free Dirac cone and quantum electrodynamics in (2+1) dimensions, Phys. Rev. Lett. 117 (2016) 016802 [arXiv:1510.08455] [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].
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. 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].
W. Wetzel, Two loop β-function for the Gross-Neveu model, Phys. Lett. B 153 (1985) 297 [INSPIRE].
J.A. Gracey, Three loop calculations in the O(N) Gross-Neveu model, Nucl. Phys. B 341 (1990) 403 [INSPIRE].
C. Luperini and P. Rossi, Three loop β-function(s) and effective potential in the Gross-Neveu model, Annals Phys. 212 (1991) 371 [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].
J.A. Gracey, Computation of critical exponent η at o(1/n 2 f ) in quantum electrodynamics in arbitrary dimensions, Nucl. Phys. B 414 (1994) 614 [hep-th/9312055] [INSPIRE].
W. Chen, M.P.A. Fisher and Y.-S. Wu, Mott transition in an anyon gas, Phys. Rev. B 48 (1993) 13749 [cond-mat/9301037] [INSPIRE].
W. Rantner and X.-G. Wen, Spin correlations in the algebraic spin liquid: Implications for high-Tc superconductors, Phys. Rev. B 66 (2002) 144501 [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].
S.S. Pufu, Anomalous dimensions of monopole operators in three-dimensional quantum electrodynamics, Phys. Rev. D 89 (2014) 065016 [arXiv:1303.6125] [INSPIRE].
Y. Huh and P. Strack, Stress tensor and current correlators of interacting conformal field theories in 2+1 dimensions: Fermionic Dirac matter coupled to U(1) gauge field, JHEP 01 (2015) 147 [Erratum ibid. 1603 (2016) 054] [arXiv:1410.1902] [INSPIRE].
S.M. Chester and S.S. Pufu, Anomalous dimensions of scalar operators in QED 3, JHEP 08 (2016) 069 [arXiv:1603.05582] [INSPIRE].
J. Polchinski, Renormalization and effective lagrangians, Nucl. Phys. B 231 (1984) 269 [INSPIRE].
C. Wetterich, Exact evolution equation for the effective potential, Phys. Lett. B 301 (1993) 90 [INSPIRE].
A.J. Niemi and G.W. Semenoff, Axial anomaly induced fermion fractionization and effective gauge theory actions in odd dimensional space-times, Phys. Rev. Lett. 51 (1983) 2077 [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].
M. Mulligan and F.J. Burnell, Topological insulators avoid the parity anomaly, Phys. Rev. B 88 (2013) 085104 [arXiv:1301.4230] [INSPIRE].
M. Franz, Z. Tesanovic and O. Vafek, QED 3 theory of pairing pseudogap in cuprates: From d-wave superconductor to antiferromagnet via ‘algebraic’ Fermi liquid, Phys. Rev. B 66 (2002) 054535 [cond-mat/0203333] [INSPIRE].
D.J. Gross and A. Neveu, Dynamical symmetry breaking in asymptotically free field theories, Phys. Rev. D 10 (1974) 3235 [INSPIRE].
J.A. Gracey, Electron mass anomalous dimension at o(1/n 2) in quantum electrodynamics, Phys. Lett. B 317 (1993) 415 [hep-th/9309092] [INSPIRE].
R. Shankar, Renormalization group approach to interacting fermions, Rev. Mod. Phys. 66 (1994) 129 [INSPIRE].
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ArXiv ePrint: 1605.05347
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Roscher, D., Torres, E. & Strack, P. Dual QED3 at “N F = 1/2” is an interacting CFT in the infrared. J. High Energ. Phys. 2016, 17 (2016). https://doi.org/10.1007/JHEP11(2016)017
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DOI: https://doi.org/10.1007/JHEP11(2016)017