Abstract
We bootstrap the deconfined quantum critical point (DQCP) and 3D Quantum Electrodynamics (QED3) coupled to Nf flavors of two-component Dirac fermions. We show the lattice and perturbative results on the SO(5) symmetric DQCP are excluded by the bootstrap bounds with an assumption that the lowest singlet scalar is irrelevant. Remarkably, we discover a new family of kinks in the 3D SO(N) vector bootstrap bounds with N ⩾ 6. We demonstrate coincidences between SU(Nf) adjoint and \( \textrm{SO}\left({N}_f^2-1\right) \) vector bootstrap bounds due to a novel algebraic relation between the crossing equations. By introducing gap assumptions breaking the \( \textrm{SO}\left({N}_f^2-1\right) \) symmetry, the SU(Nf) adjoint bootstrap bounds with large Nf converge to the 1/Nf perturbative results of QED3. Our results provide strong evidence that the SO(5) DQCP is not continuous and the critical flavor number of QED3 is slightly above 2: \( {N}_f^{\ast}\in \left(2,4\right) \). Bootstrap results near \( {N}_f^{\ast } \) are well consistent with the merger and annihilation mechanism for the loss of conformality in QED3.
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References
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].
R.D. Pisarski, Chiral Symmetry Breaking in Three-Dimensional Electrodynamics, Phys. Rev. D 29 (1984) 2423 [INSPIRE].
T.W. Appelquist, M.J. Bowick, D. Karabali and L.C.R. Wijewardhana, Spontaneous Chiral Symmetry Breaking in Three-Dimensional QED, Phys. Rev. D 33 (1986) 3704 [INSPIRE].
W. Rantner and X.-G. Wen, Electron spectral function and algebraic spin liquid for the normal state of underdoped high Tc 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-Tc superconductors, Phys. Rev. B 66 (2002) 144501 [cond-mat/0201521] [INSPIRE].
K.-i. Kubota and H. Terao, Dynamical symmetry breaking in QED3 from the Wilson RG point of view, Prog. Theor. Phys. 105 (2001) 809 [hep-ph/0101073] [INSPIRE].
A.V. Kotikov, V.I. Shilin and S. Teber, Critical behavior of (2 + 1)-dimensional QED: 1/Nf corrections in the Landau gauge, Phys. Rev. D 94 (2016) 056009 [Erratum ibid. 99 (2019) 119901] [arXiv:1605.01911] [INSPIRE].
K. Kaveh and I.F. Herbut, Chiral symmetry breaking in QED3 in presence of irrelevant interactions: A Renormalization group study, Phys. Rev. B 71 (2005) 184519 [cond-mat/0411594] [INSPIRE].
S. Giombi, I.R. Klebanov and G. Tarnopolsky, Conformal QEDd , F -Theorem and the ϵ Expansion, J. Phys. A 49 (2016) 135403 [arXiv:1508.06354] [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, G. Tarnopolsky and I.R. Klebanov, On CJ and CT in Conformal QED, JHEP 08 (2016) 156 [arXiv:1602.01076] [INSPIRE].
N. Zerf, P. Marquard, R. Boyack and J. Maciejko, Critical behavior of the QED3-Gross-Neveu-Yukawa model at four loops, Phys. Rev. B 98 (2018) 165125 [arXiv:1808.00549] [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].
S. Benvenuti and H. Khachatryan, Qed’s in 2+1 dimensions: complex fixed points and dualities, arXiv:1812.01544.
J. Braun, H. Gies, L. Janssen and D. Roscher, Phase structure of many-flavor QED3, Phys. Rev. D 90 (2014) 036002 [arXiv:1404.1362] [INSPIRE].
S. Gukov, RG Flows and Bifurcations, Nucl. Phys. B 919 (2017) 583 [arXiv:1608.06638] [INSPIRE].
S.J. Hands, J.B. Kogut, L. Scorzato and C.G. Strouthos, The Chiral limit of noncompact QED in three-dimensions, Nucl. Phys. B Proc. Suppl. 119 (2003) 974 [hep-lat/0209133] [INSPIRE].
S.J. Hands, J.B. Kogut and C.G. Strouthos, Noncompact QED3 with Nf greater than or equal to 2, Nucl. Phys. B 645 (2002) 321 [hep-lat/0208030] [INSPIRE].
S.J. Hands, J.B. Kogut, L. Scorzato and C.G. Strouthos, Non-compact QED3 with Nf = 1 and Nf = 4, Phys. Rev. B 70 (2004) 104501 [hep-lat/0404013] [INSPIRE].
C. Strouthos and J.B. Kogut, The Phases of Non-Compact QED3, PoS LATTICE2007 (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].
N. Karthik and R. Narayanan, Scale-invariance of parity-invariant three-dimensional QED, Phys. Rev. D 94 (2016) 065026 [arXiv:1606.04109] [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] [INSPIRE].
A. Karch and D. Tong, Particle-Vortex Duality from 3d Bosonization, Phys. Rev. X 6 (2016) 031043 [arXiv:1606.01893] [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].
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].
T. Senthil, D.T. Son, C. Wang and C. Xu, Duality between (2 + 1)d Quantum Critical Points, Phys. Rept. 827 (2019) 1 [arXiv:1810.05174] [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].
Y.Q. Qin et al., Duality between the deconfined quantum-critical point and the bosonic topological transition, Phys. Rev. X 7 (2017) 031052 [arXiv:1705.10670] [INSPIRE].
G.J. Sreejith, S. Powell and A. Nahum, Emergent SO(5) symmetry at the columnar ordering transition in the classical cubic dimer model, Phys. Rev. Lett. 122 (2019) 080601 [arXiv:1803.11218] [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].
X.Y. Xu, Y. Qi, L. Zhang, F.F. Assaad, C. Xu and Z.Y. Meng, Monte Carlo Study of Lattice Compact Quantum Electrodynamics with Fermionic Matter: The Parent State of Quantum Phases, Phys. Rev. X 9 (2019) 021022 [arXiv:1807.07574] [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].
D. Poland, S. Rychkov and A. Vichi, The Conformal Bootstrap: Theory, Numerical Techniques, and Applications, Rev. Mod. Phys. 91 (2019) 015002 [arXiv:1805.04405] [INSPIRE].
S.M. Chester and S.S. Pufu, Towards bootstrapping QED3, JHEP 08 (2016) 019 [arXiv:1601.03476] [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].
Y. Nakayama and T. Ohtsuki, Conformal Bootstrap Dashing Hopes of Emergent Symmetry, Phys. Rev. Lett. 117 (2016) 131601 [arXiv:1602.07295] [INSPIRE].
Y. Nakayama, unpublished.
D. Simmons-Duffin, unpublished.
D. Poland, unpublished.
A.W. Sandvik, Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions, Phys. Rev. Lett. 98 (2007) 227202 [cond-mat/0611343] [INSPIRE].
R.G. Melko and R.K. Kaul, Scaling in the fan of an unconventional quantum critical point, Phys. Rev. Lett. 100 (2008).
S. Pujari, K. Damle and F. Alet, Néel-state to valence-bond-solid transition on the honeycomb lattice: Evidence for deconfined criticality, Phys. Rev. Lett. 111 (2013).
E. Dyer, M. Mezei, S.S. Pufu and S. Sachdev, Scaling dimensions of monopole operators in the \( {\mathbbm{CP}}^{N_b-1} \) theory in 2 + 1 dimensions, JHEP 06 (2015) 037 [Erratum ibid. 03 (2016) 111] [arXiv:1504.00368] [INSPIRE].
E. Dupuis, R. Boyack and W. Witczak-Krempa, Anomalous Dimensions of Monopole Operators at the Transitions between Dirac and Topological Spin Liquids, Phys. Rev. X 12 (2022) 031012 [arXiv:2108.05922] [INSPIRE].
R. Boyack, A. Rayyan and J. Maciejko, Deconfined criticality in the QED3 Gross-Neveu-Yukawa model: The 1/N expansion revisited, Phys. Rev. B 99 (2019) 195135 [arXiv:1812.02720] [INSPIRE].
D. Simmons-Duffin, A Semidefinite Program Solver for the Conformal Bootstrap, JHEP 06 (2015) 174 [arXiv:1502.02033] [INSPIRE].
F. Kos, D. Poland and D. Simmons-Duffin, Bootstrapping the O(N) vector models, JHEP 06 (2014) 091 [arXiv:1307.6856] [INSPIRE].
H. Gies and J. Jaeckel, Chiral phase structure of QCD with many flavors, Eur. Phys. J. C 46 (2006) 433 [hep-ph/0507171] [INSPIRE].
D.B. Kaplan, J.-W. Lee, D.T. Son and M.A. Stephanov, Conformality Lost, Phys. Rev. D 80 (2009) 125005 [arXiv:0905.4752] [INSPIRE].
V. Gorbenko, S. Rychkov and B. Zan, Walking, Weak first-order transitions, and Complex CFTs, JHEP 10 (2018) 108 [arXiv:1807.11512] [INSPIRE].
J.A. Gracey, Fermion bilinear operator critical exponents at O(1/N2) in the QED-Gross-Neveu universality class, Phys. Rev. D 98 (2018) 085012 [arXiv:1808.07697] [INSPIRE].
Z. Li and D. Poland, Searching for gauge theories with the conformal bootstrap, JHEP 03 (2021) 172 [arXiv:2005.01721] [INSPIRE].
Z. Li, Symmetries of conformal correlation functions, Phys. Rev. D 105 (2022) 085018 [arXiv:2006.05119] [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].
H. Iha, H. Makino and H. Suzuki, Upper bound on the mass anomalous dimension in many-flavor gauge theories: a conformal bootstrap approach, PTEP 2016 (2016) 053B03 [arXiv:1603.01995] [INSPIRE].
F.A. Dolan and H. Osborn, Conformal four point functions and the operator product expansion, Nucl. Phys. B 599 (2001) 459 [hep-th/0011040] [INSPIRE].
F.A. Dolan and H. Osborn, Conformal partial waves and the operator product expansion, Nucl. Phys. B 678 (2004) 491 [hep-th/0309180] [INSPIRE].
C. Xu, Renormalization group studies on four-fermion interaction instabilities on algebraic spin liquids, Phys. Rev. B 78 (2008) 054432.
S.M. Chester and S.S. Pufu, Anomalous dimensions of scalar operators in QED3, JHEP 08 (2016) 069 [arXiv:1603.05582] [INSPIRE].
J.Y. Lee, C. Wang, M.P. Zaletel, A. Vishwanath and Y.-C. He, Emergent Multi-flavor QED3 at the Plateau Transition between Fractional Chern Insulators: Applications to graphene heterostructures, Phys. Rev. X 8 (2018) 031015 [arXiv:1802.09538] [INSPIRE].
V. Gorbenko, S. Rychkov and B. Zan, Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model at Q > 4, SciPost Phys. 5 (2018) 050 [arXiv:1808.04380] [INSPIRE].
D. Poland, D. Simmons-Duffin and A. Vichi, Carving Out the Space of 4D CFTs, JHEP 05 (2012) 110 [arXiv:1109.5176] [INSPIRE].
Y. Nakayama, Bootstrap experiments on higher dimensional CFTs, Int. J. Mod. Phys. A 33 (2018) 1850036 [arXiv:1705.02744] [INSPIRE].
J.A. Gracey, Electron mass anomalous dimension at\( O\Big(1/\left({N}_f^2\right) \) in quantum electrodynamics, Phys. Lett. B 317 (1993) 415 [hep-th/9309092] [INSPIRE].
Z. Li and N. Su, 3D CFT Archipelago from Single Correlator Bootstrap, Phys. Lett. B 797 (2019) 134920 [arXiv:1706.06960] [INSPIRE].
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Li, Z. Bootstrapping conformal QED3 and deconfined quantum critical point. J. High Energ. Phys. 2022, 5 (2022). https://doi.org/10.1007/JHEP11(2022)005
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DOI: https://doi.org/10.1007/JHEP11(2022)005