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  • Letter
  • Open Access

Evidence for web of dualities from monopole operators

Shai M. Chester

Éric Dupuis

William Witczak-Krempa

  • Jefferson Physical Laboratory, Harvard University, Cambridge, Massachusetts 02138, USA and Center of Mathematical Sciences and Applications, Harvard University, Cambridge, Massachusetts 02138, USA

  • Département de physique, Université de Montréal, Montréal H3C 3J7, Quebec, Canada

  • Département de physique, Université de Montréal, Montréal H3C 3J7, Quebec, Canada; Centre de Recherches Mathématiques, Université de Montréal, Montréal H3C 3J7, Quebec, Canada; and Institut Courtois, Université de Montréal, Montréal H2V 0B3, Quebec, Canada

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Phys. Rev. D 108, L021701 – Published 5 July, 2023

DOI: https://doi.org/10.1103/PhysRevD.108.L021701

Abstract

We give evidence for the web of 3d bosonization dualities in conformal field theories (CFTs) by computing monopole operator scaling dimensions in (2+1)-dimensional quantum electrodynamics (QED3) with Chern-Simons level k and N complex bosons in a large-N, k expansion. We first consider the k=0 case, where we show that scaling dimensions previously computed to subleading order in 1/N can be extrapolated to N=1 and matched to O(2) Wilson-Fisher CFT scaling dimensions with around 5% error, which is evidence for particle-vortex duality. We then generalize the subleading calculation to large N, k and fixed k/N, extrapolate to N=k=1, and consider monopole operators that are conjectured to be dual to nondegenerate scalar operators in a theory of a single Dirac fermion. We find matches typically with 1% error or less, which is strong evidence of this so-called “seed” duality that implies a web of 3d bosonization dualities among CFTs.

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References (58)

  1. M. E. Peskin, Mandelstam ’t Hooft duality in Abelian lattice models, Ann. Phys. (N.Y.) 113, 122 (1978).
  2. C. Dasgupta and B. I. Halperin, Phase Transition in a Lattice Model of Superconductivity, Phys. Rev. Lett. 47, 1556 (1981).
  3. D. T. Son, Is the Composite Fermion a Dirac Particle?, Phys. Rev. X 5, 031027 (2015).
  4. W. Chen, M. P. A. Fisher, and Y.-S. Wu, Mott transition in an anyon gas, Phys. Rev. B 48, 13749 (1993).
  5. M. Barkeshli and J. McGreevy, Continuous transition between fractional quantum Hall and superfluid states, Phys. Rev. B 89, 235116 (2014).
  6. A. Karch and D. Tong, Particle-Vortex Duality from 3d Bosonization, Phys. Rev. X 6, 031043 (2016).
  7. N. Seiberg, T. Senthil, C. Wang, and E. Witten, A duality web in 2+1 dimensions and condensed matter physics, Ann. Phys. (Amsterdam) 374, 395 (2016).
  8. K. Kajantie, M. Laine, T. Neuhaus, A. Rajantie, and K. Rummukainen, Duality and scaling in three-dimensional scalar electrodynamics, Nucl. Phys. B699, 632 (2004).
  9. N. Karthik, Monopole scaling dimension using Monte-Carlo simulation, Phys. Rev. D 98, 074513 (2018).
  10. M. Hasenbusch, Monte Carlo study of an improved clock model in three dimensions, Phys. Rev. B 100, 224517 (2019).
  11. D. Banerjee, S. Chandrasekharan, and D. Orlando, Conformal Dimensions via Large Charge Expansion, Phys. Rev. Lett. 120, 061603 (2018).

  12. The O(2) lattice studies in fact have more precision than shown here, as we show later in Table 1.

  13. G. Gur-Ari and R. Yacoby, Three dimensional bosonization from supersymmetry, J. High Energy Phys. 11 (2015) 013.
  14. S. Kachru, M. Mulligan, G. Torroba, and H. Wang, Bosonization and mirror symmetry, Phys. Rev. D 94, 085009 (2016).
  15. A. Giveon and D. Kutasov, Seiberg duality in Chern-Simons theory, Nucl. Phys. B812, 1 (2009).
  16. O. Aharony, Baryons, monopoles and dualities in Chern-Simons-matter theories, J. High Energy Phys. 02 (2016) 093.
  17. O. Aharony, G. Gur-Ari, and R. Yacoby, Correlation functions of large N Chern-Simons-matter theories and bosonization in three dimensions, J. High Energy Phys. 12 (2012) 028.
  18. O. Aharony, G. Gur-Ari, and R. Yacoby, d=3 bosonic vector models coupled to Chern-Simons gauge theories, J. High Energy Phys. 03 (2012) 037.
  19. 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, 2112 (2012).
  20. G. Murthy and S. Sachdev, Action of hedgehog instantons in the disordered phase of the (2+1)-dimensional CPN−1 model, Nucl. Phys. B344, 557 (1990).
  21. V. Borokhov, A. Kapustin, and X.-k. Wu, Topological disorder operators in three-dimensional conformal field theory, J. High Energy Phys. 11 (2002) 049.
  22. E. Dyer, M. Mezei, S. S. Pufu, and S. Sachdev, Scaling dimensions of monopole operators in the CPNb−1 theory in 2+1 dimensions, J. High Energy Phys. 06 (2015) 037.
  23. S. M. Chester, W. Landry, J. Liu, D. Poland, D. Simmons-Duffin, N. Su, and A. Vichi, Carving out OPE space and precise O(2) model critical exponents, J. High Energy Phys. 06 (2020) 142.
  24. J. Liu, D. Meltzer, D. Poland, and D. Simmons-Duffin, The Lorentzian inversion formula and the spectrum of the 3d O(2) CFT, J. High Energy Phys. 09 (2020) 115; 01 (2021) 206(E).
  25. S. M. Chester, L. V. Iliesiu, M. Mezei, and S. S. Pufu, Monopole operators in U(1) Chern-Simons-matter theories, J. High Energy Phys. 05 (2018) 157.

  26. The subleading calculation was previously computed at large N, k for the specific case of κ=1 for the lowest charged monopole [27], but this is dual to a free fermion operator, not a scalar, and so did not match the conjectured duality.

  27. S. M. Chester, Anomalous dimensions of monopole operators in scalar QED3 with Chern-Simons term, J. High Energy Phys. 07 (2021) 034.
  28. A. De La Fuente, The large charge expansion at large N, J. High Energy Phys. 08 (2018) 041.
  29. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevD.108.L021701 for more technical details of the calculation.
  30. A. M. Polyakov, Compact gauge fields and the infrared catastrophe, Phys. Lett. 59B, 82 (1975).
  31. S. S. Pufu, Anomalous dimensions of monopole operators in three-dimensional quantum electrodynamics, Phys. Rev. D 89, 065016 (2014).
  32. E. Dyer, M. Mezei, and S. S. Pufu, Monopole taxonomy in three-dimensional conformal field theories, arXiv:1309.1160.
  33. S. M. Chester, M. Mezei, S. S. Pufu, and I. Yaakov, Monopole operators from the 4−ε expansion, J. High Energy Phys. 12 (2016) 015.
  34. M. A. Metlitski, M. Hermele, T. Senthil, and M. P. Fisher, Monopoles in CPN−1 model via the state-operator correspondence, Phys. Rev. B 78, 214418 (2008).
  35. V. Borokhov, A. Kapustin, and X.-k. Wu, Monopole operators and mirror symmetry in three dimensions, J. High Energy Phys. 12 (2002) 044.
  36. E. Dupuis, M. B. Paranjape, and W. Witczak-Krempa, Transition from a Dirac spin liquid to an antiferromagnet: Monopoles in a QED3-Gross-Neveu theory, Phys. Rev. B 100, 094443 (2019).
  37. E. Dupuis, M. B. Paranjape, and W. Witczak-Krempa, Monopole operators and their symmetries in QED3-Gross–Neveu models, in Proceedings of the 11th International Symposium on Quantum Theory and Symmetries (2019), arXiv:1911.05802.
  38. E. Dupuis and W. Witczak-Krempa, Monopole hierarchy in transitions out of a Dirac spin liquid, Ann. Phys. (Amsterdam) 435, 168496 (2021).
  39. 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, 031012 (2022).

  40. QED3 was shown to flow to an IR CFT at large N [41], and this behavior is believed to persist at finite N except perhaps for N=2 and k=0.

  41. T. Appelquist, D. Nash, and L. Wijewardhana, Critical Behavior in (2+1)-Dimensional QED, Phys. Rev. Lett. 60, 2575 (1988).

  42. The large N results are shown to 5 significant digits for κ=0 and 4 digits for κ=1, but any number of digits can be computed in principle. The bootstrap results for q=1/2, 1 are rigorous [23], while for q=3/2, 2 they were non-rigorously extracted from the spectrum and so have an uncertainty [24]. The lattice results in [10, 11] are less precise, and we give their uncertainty.

  43. For this duality, the parity symmetry that is manifest in the free fermion comes from the duality of k=1 QED3 to k=−1 [7]. The monopole scaling dimension calculation only depends on |k|, so it automatically respects this parity duality.

  44. F. Dolan, Character formulae and partition functions in higher dimensional conformal field theory, J. Math. Phys. (N.Y.) 47, 062303 (2006).
  45. Z. Komargodski, M. Mezei, S. Pal, and A. Raviv-Moshe, Spontaneously broken boosts in CFTs, J. High Energy Phys. 09 (2021) 064.
  46. S. Hellerman, D. Orlando, S. Reffert, and M. Watanabe, On the CFT operator spectrum at large global charge, J. High Energy Phys. 12 (2015) 071.
  47. G. Cuomo, L. V. Delacretaz, and U. Mehta, Large charge sector of 3d parity-violating CFTs, J. High Energy Phys. 05 (2021) 115.

  48. The large N expansion also works well for some sphere free energies in 3d [49].

  49. I. R. Klebanov, S. S. Pufu, S. Sachdev, and B. R. Safdi, Entanglement entropy of 3-d conformal gauge theories with many flavors, J. High Energy Phys. 05 (2012) 036.
  50. 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, 292 (1974).

  51. As discussed in [7], to properly define QED3 in this case one must add various gravitational Chern-Simons terms, but these do not contribute the local CFT data we are interested in

  52. C. Wang, A. Nahum, M. A. Metlitski, C. Xu, and T. Senthil, Deconfined Quantum Critical Points: Symmetries and Dualities, Phys. Rev. X 7, 031051 (2017).

  53. Some evidence from monopole scaling dimensions was found in [39] for the duality between Gross-Neveu QED3 with two fermions and scalar QED3 with two scalars, but it is unclear if the latter theory is in fact a CFT [54, 55, 56], which is a prerequisite for IR duality.

  54. B. Zhao, P. Weinberg, and A. W. Sandvik, Symmetry-enhanced discontinuous phase transition in a two-dimensional quantum magnet, Nat. Phys. 15, 678 (2019).
  55. 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, 195110 (2019).
  56. F. Kos, D. Poland, and D. Simmons-Duffin, Bootstrapping the O(N) vector models, J. High Energy Phys. 06 (2014) 091.
  57. O. Aharony, F. Benini, P.-S. Hsin, and N. Seiberg, Chern-Simons-matter dualities with SO and USp gauge groups, J. High Energy Phys. 02 (2017) 072.
  58. F. Benini and S. Benvenuti, N=1 dualities in 2+1 dimensions, J. High Energy Phys. 11 (2018) 197.

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Phys. Rev. D 108, L021701– Published 5 July, 2023
  • Received 1 November 2022
  • Accepted 9 June 2023
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