Abstract
We initiate the conformal bootstrap study of Quantum Electrodynamics in 2+1 space-time dimensions (QED3) with N flavors of charged fermions by focusing on the 4-point function of four monopole operators with the lowest unit of topological charge. We obtain upper bounds on the scaling dimension of the doubly-charged monopole operator, with and without assuming other gaps in the operator spectrum. Intriguingly, we find a (gap-dependent) kink in these bounds that comes reasonably close to the large N extrapolation of the scaling dimensions of the singly-charged and doubly-charged monopole operators down to N = 4 and N = 6.
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References
R.D. Pisarski, Chiral symmetry breaking in three-dimensional electrodynamics, Phys. Rev. D 29 (1984) 2423 [INSPIRE].
A.M. Polyakov, Compact gauge fields and the infrared catastrophe, Phys. Lett. B 59 (1975) 82 [INSPIRE].
A.M. Polyakov, Quark confinement and topology of gauge groups, Nucl. Phys. B 120 (1977) 429 [INSPIRE].
T. Appelquist, D. Nash and L.C.R. Wijewardhana, Critical behavior in (2 + 1)-dimensional QED, Phys. Rev. Lett. 60 (1988) 2575 [INSPIRE].
D. Nash, Higher order corrections in (2 + 1)-dimensional QED, Phys. Rev. Lett. 62 (1989) 3024 [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].
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].
S.J. Hands, J.B. Kogut, L. Scorzato and C.G. Strouthos, Non-compact QED 3 with N f = 1 and N f = 4, Phys. Rev. B 70 (2004) 104501 [hep-lat/0404013] [INSPIRE].
C. Strouthos and J.B. Kogut, The phases of non-compact QED 3, PoS (LATTICE 2007) 278 [arXiv:0804.0300] [INSPIRE].
N. Karthik and R. Narayanan, No evidence for bilinear condensate in parity-invariant three-dimensional QED with massless fermions, Phys. Rev. D 93 (2016) 045020 [arXiv:1512.02993] [INSPIRE].
R. Rattazzi, V.S. Rychkov, E. Tonni and A. Vichi, Bounding scalar operator dimensions in 4D CFT, JHEP 12 (2008) 031 [arXiv:0807.0004] [INSPIRE].
F. Kos, D. Poland and D. Simmons-Duffin, Bootstrapping mixed correlators in the 3D Ising model, JHEP 11 (2014) 109 [arXiv:1406.4858] [INSPIRE].
F. Kos, D. Poland and D. Simmons-Duffin, Bootstrapping the O(N) vector models, JHEP 06 (2014) 091 [arXiv:1307.6856] [INSPIRE].
F. Kos, D. Poland, D. Simmons-Duffin and A. Vichi, Bootstrapping the O(N) archipelago, JHEP 11 (2015) 106 [arXiv:1504.07997] [INSPIRE].
S.M. Chester, S.S. Pufu and R. Yacoby, Bootstrapping O(N) vector models in 4 < d < 6, Phys. Rev. D 91 (2015) 086014 [arXiv:1412.7746] [INSPIRE].
L. Iliesiu, F. Kos, D. Poland, S.S. Pufu, D. Simmons-Duffin and R. Yacoby, Bootstrapping 3D fermions, JHEP 03 (2016) 120 [arXiv:1508.00012] [INSPIRE].
M. Berkooz, R. Yacoby and A. Zait, Bounds on N = 1 superconformal theories with global symmetries, JHEP 08 (2014) 008 [Erratum ibid. 01 (2015) 132] [arXiv:1402.6068] [INSPIRE].
D. Simmons-Duffin, A semidefinite program solver for the conformal bootstrap, JHEP 06 (2015) 174 [arXiv:1502.02033] [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].
E. Dyer, M. Mezei and S.S. Pufu, Monopole taxonomy in three-dimensional conformal field theories, arXiv:1309.1160 [INSPIRE].
X.-G. Wen and Y.-S. Wu, Transitions between the quantum Hall states and insulators induced by periodic potentials, Phys. Rev. Lett. 70 (1993) 1501 [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].
S. Sachdev, Nonzero temperature transport near fractional quantum Hall critical points, Phys. Rev. B 57 (1998) 7157 [cond-mat/9709243] [INSPIRE].
W. Rantner and X.-G. Wen, Electron spectral function and algebraic spin liquid for the normal state of underdoped high T c superconductors, Phys. Rev. Lett. 86 (2001) 3871 [cond-mat/0010378] [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 [INSPIRE].
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].
T. Senthil, A. Vishwanath, L. Balents, S. Sachdev and M.P.A. Fisher, Deconfined quantum critical points, Science 303 (2004) 1490 [cond-mat/0311326].
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].
M. Hermele, T. Senthil, M.P.A. Fisher, P.A. Lee, N. Nagaosa and X.-G. Wen, Stability of U(1) spin liquids in two dimensions, Phys. Rev. B 70 (2004) 214437 [cond-mat/0404751] [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 [cond-mat/0502215] [INSPIRE].
Y. Ran and X.-G. Wen, Continuous quantum phase transitions beyond Landau’s paradigm in a large-N spin model, cond-mat/0609620.
R.K. Kaul, Y.B. Kim, S. Sachdev and T. Senthil, Algebraic charge liquids, Nature Phys. 4 (2008) 28 [arXiv:0706.2187].
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. Sachdev, The landscape of the Hubbard model, arXiv:1012.0299 [INSPIRE].
S.M. Chester, M. Mezei, S.S. Pufu and I. Yaakov, Monopole operators from the 4 − ϵ expansion, arXiv:1511.07108 [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].
M.A. Metlitski, M. Hermele, T. Senthil and M.P.A. Fisher, Monopoles in CP N −1 model via the state-operator correspondence, Phys. Rev. B 78 (2008) 214418 [arXiv:0809.2816] [INSPIRE].
S.S. Pufu, Anomalous dimensions of monopole operators in three-dimensional quantum electrodynamics, Phys. Rev. D 89 (2014) 065016 [arXiv:1303.6125] [INSPIRE].
S.S. Pufu and S. Sachdev, Monopoles in 2 + 1-dimensional conformal field theories with global U(1) symmetry, JHEP 09 (2013) 127 [arXiv:1303.3006] [INSPIRE].
E. Dyer, M. Mezei, S.S. Pufu and S. Sachdev, Scaling dimensions of monopole operators in the CP Nb–1 theory in 2 + 1 dimensions, JHEP 06 (2015) 037 [Erratum ibid. 03 (2016) 111] [arXiv:1504.00368] [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].
J.A. Gracey, Electron mass anomalous dimension at O(1/N 2 f ) in quantum electrodynamics, Phys. Lett. B 317 (1993) 415 [hep-th/9309092] [INSPIRE].
C. Strouthos and J.B. Kogut, Chiral symmetry breaking in three dimensional QED, J. Phys. Conf. Ser. 150 (2009) 052247 [arXiv:0808.2714] [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.M. Chester and S.S. Pufu, Anomalous dimensions of scalar operators in QED 3, arXiv:1603.05582 [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. Giombi, G. Tarnopolsky and I.R. Klebanov, On C J and C T in conformal QED, arXiv:1602.01076 [INSPIRE].
Y. Huh, P. Strack and S. Sachdev, Conserved current correlators of conformal field theories in 2 + 1 dimensions, Phys. Rev. B 88 (2013) 155109 [Erratum ibid. B 90 (2014) 199902] [arXiv:1307.6863] [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. 03 (2016) 054] [arXiv:1410.1902] [INSPIRE].
R. Rattazzi, S. Rychkov and A. Vichi, Bounds in 4D conformal field theories with global symmetry, J. Phys. A 44 (2011) 035402 [arXiv:1009.5985] [INSPIRE].
M. Hogervorst and S. Rychkov, Radial coordinates for conformal blocks, Phys. Rev. D 87 (2013) 106004 [arXiv:1303.1111] [INSPIRE].
S.M. Chester, J. Lee, S.S. Pufu and R. Yacoby, The N = 8 superconformal bootstrap in three dimensions, JHEP 09 (2014) 143 [arXiv:1406.4814] [INSPIRE].
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Chester, S.M., Pufu, S.S. Towards bootstrapping QED3 . J. High Energ. Phys. 2016, 19 (2016). https://doi.org/10.1007/JHEP08(2016)019
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DOI: https://doi.org/10.1007/JHEP08(2016)019