Abstract
In 2 + 1-dimensional conformal field theories with a global U(1) symmetry, monopoles can be introduced through a background gauge field that couples to the U(1) conserved current. We use the state-operator correspondence to calculate scaling dimensions of such monopole insertions. We obtain the next-to-leading term in the 1/N b expansion of the Wilson-Fisher fixed point in the theory of N b complex bosons.
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References
A.M. Polyakov, Compact gauge fields and the infrared catastrophe, Phys. Lett. B 59 (1975) 82 [INSPIRE].
G. Baskaran and P.W. Anderson, Gauge theory of high temperature superconductors and strongly correlated Fermi systems, Phys. Rev. B 37 (1988) 580 [INSPIRE].
F. Haldane, O(3) nonlinear σ-model and the topological distinction between integer- and half-integer-spin antiferromagnets in two dimensions, Phys. Rev. Lett. 61 (1988) 1029 [INSPIRE].
N. Read and S. Sachdev, Valence-bond and spin-Peierls ground states of low-dimensional quantum antiferromagnets, Phys. Rev. Lett. 62 (1989) 1694 [INSPIRE].
N. Read and S. Sachdev, Spin-Peierls, valence-bond solid and Neel ground states of low-dimensional quantum antiferromagnets, Phys. Rev. B 42 (1990) 4568 [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].
V. Borokhov, A. Kapustin and X.-k. Wu, Monopole operators and mirror symmetry in three-dimensions, JHEP 12 (2002) 044 [hep-th/0207074] [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), no. 14 144407 [cond-mat/0312617].
M.A. Metlitski, M. Hermele, T. Senthil and M.P. Fisher, Monopoles in CP N −1 model via the state-operator correspondence, Phys. Rev. B 78 (2008) 214418 [arXiv:0809.2816] [INSPIRE].
M. Hermele, Non-abelian descendant of abelian duality in a two-dimensional frustrated quantum magnet, Phys. Rev. B 79 (2009) 184429 [arXiv:0902.1350] [INSPIRE].
M.K. Benna, I.R. Klebanov and T. Klose, Charges of monopole operators in Chern-Simons Yang-Mills theory, JHEP 01 (2010) 110 [arXiv:0906.3008] [INSPIRE].
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].
S. Pujari, K. Damle and F. Alet, Néel to valence-bond solid transition on the honeycomb lattice: evidence for deconfined criticality, arXiv:1302.1408.
A. Kapustin and B. Willett, Generalized superconformal index for three dimensional field theories, arXiv:1106.2484 [INSPIRE].
S. Sachdev, Compressible quantum phases from conformal field theories in 2 + 1 dimensions, Phys. Rev. D 86 (2012) 126003 [arXiv:1209.1637] [INSPIRE].
T. Faulkner and N. Iqbal, Friedel oscillations and horizon charge in 1D holographic liquids, JHEP 07 (2013) 060 [arXiv:1207.4208] [INSPIRE].
J. Polchinski and E. Silverstein, Large-density field theory, viscosity and ’2k F ’ singularities from string duals, Class. Quant. Grav. 29 (2012) 194008 [arXiv:1203.1015] [INSPIRE].
L. Huijse and S. Sachdev, Fermi surfaces and gauge-gravity duality, Phys. Rev. D 84 (2011) 026001 [arXiv:1104.5022] [INSPIRE].
N. Ogawa, T. Takayanagi and T. Ugajin, Holographic Fermi surfaces and entanglement entropy, JHEP 01 (2012) 125 [arXiv:1111.1023] [INSPIRE].
L. Huijse, S. Sachdev and B. Swingle, Hidden Fermi surfaces in compressible states of gauge-gravity duality, Phys. Rev. B 85 (2012) 035121 [arXiv:1112.0573] [INSPIRE].
T.T. Wu and C.N. Yang, Dirac monopole without strings: monopole harmonics, Nucl. Phys. B 107 (1976) 365 [INSPIRE].
T.T. Wu and C.N. Yang, Some properties of monopole harmonics, Phys. Rev. D 16 (1977) 1018 [INSPIRE].
M. Campostrini, M. Hasenbusch, A. Pelissetto, P. Rossi and E. Vicari, Critical behavior of the three-dimensional xy universality class, Phys. Rev. B 63 (2001) 214503 [cond-mat/0010360] [INSPIRE].
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ArXiv ePrint: 1303.3006
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Pufu, S.S., Sachdev, S. Monopoles in 2 + 1-dimensional conformal field theories with global U(1) symmetry. J. High Energ. Phys. 2013, 127 (2013). https://doi.org/10.1007/JHEP09(2013)127
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DOI: https://doi.org/10.1007/JHEP09(2013)127