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Matrix models at large charge

A preprint version of the article is available at arXiv.

Abstract

We show that the large-charge formalism can be successfully applied to models that go beyond the vector models discussed so far in the literature. We study the explicit example of a conformal SU(3) matrix model in 2+1 space-time dimensions at fixed charge and calculate the anomalous dimension and fusion coefficients at leading order in the U(1) charge.

References

  1. S. Hellerman, D. Orlando, S. Reffert and M. Watanabe, On the CFT Operator Spectrum at Large Global Charge, JHEP 12 (2015) 071 [arXiv:1505.01537] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  2. L. Álvarez-Gaumé, O. Loukas, D. Orlando and S. Reffert, Compensating strong coupling with large charge, JHEP 04 (2017) 059 [arXiv:1610.04495] [INSPIRE].

    MathSciNet  Article  Google Scholar 

  3. D. Banerjee, S. Chandrasekharan and D. Orlando, Conformal dimensions via large charge expansion, arXiv:1707.00711 [INSPIRE].

  4. O. Loukas, Abelian scalar theory at large global charge, Fortsch. Phys. 65 (2017) 1700028 [arXiv:1612.08985] [INSPIRE].

    MathSciNet  Article  Google Scholar 

  5. A. Monin, D. Pirtskhalava, R. Rattazzi and F.K. Seibold, Semiclassics, Goldstone Bosons and CFT data, JHEP 06 (2017) 011 [arXiv:1611.02912] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  6. S. Hellerman, N. Kobayashi, S. Maeda and M. Watanabe, A Note on Inhomogeneous Ground States at Large Global Charge, arXiv:1705.05825 [INSPIRE].

  7. S. Hellerman, S. Maeda and M. Watanabe, Operator Dimensions from Moduli, arXiv:1706.05743 [INSPIRE].

  8. S. Coleman, Aspects Of Symmetry, Cambridge University Press, Cambridge U.K. (1988).

  9. K.I. Kugel’ and D.I. Khomskii, The Jahn-Teller effect and magnetism: transition metal compounds, Phys. Usp. 25 (1982) 231.

  10. A.V. Gorshkov et al., Two-orbital SU(N ) magnetism with ultracold alkaline-earth atoms, Nature Phys. 6 (2010) 289 [arXiv:0905.2610].

    ADS  Article  Google Scholar 

  11. C. Laflamme et al., ℂP(N − 1) quantum field theories with alkaline-earth atoms in optical lattices, Annals Phys. 370 (2016) 117 [arXiv:1507.06788] [INSPIRE].

  12. M. Kamal and G. Murthy, New O(3) transition in three dimensions, Phys. Rev. Lett. 71 (1993)1911.

  13. 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].

  14. A. Nahum, J.T. Chalker, P. Serna, M. Ortuño and A.M. Somoza, Phase transitions in three-dimensional loop models and the CP n−1 σ-model, Phys. Rev. B 88 (2013) 134411 [arXiv:1308.0144] [INSPIRE].

    ADS  Article  Google Scholar 

  15. 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].

  16. N. Read and S. Sachdev, Spin-Peierls, valence-bond solid and Néel ground states of low-dimensional quantum antiferromagnets, Phys. Rev. B 42 (1990) 4568 [INSPIRE].

    ADS  Article  Google Scholar 

  17. 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].

    ADS  Article  Google Scholar 

  18. 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].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  19. E. Dyer, M. Mezei, S.S. Pufu and S. Sachdev, Scaling dimensions of monopole operators in the \( \mathbb{C}{\mathrm{P}}^{N_{b-1}} \) theory in 2 + 1 dimensions, JHEP 06 (2015) 037 [Erratum ibid. 1603 (2016) 111] [arXiv:1504.00368] [INSPIRE].

  20. T. Senthil et al., Deconfined Quantum Critical Points, Science 303 (2004) 1490 [cond-mat/0311326].

  21. T. Senthil et al., Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm, Phys. Rev. B 70 (2004) 144407.

    ADS  Article  Google Scholar 

  22. F. Delfino, A. Pelissetto and E. Vicari, Three-dimensional antiferromagnetic CP N −1 models, Phys. Rev. E 91 (2015) 052109 [arXiv:1502.07599] [INSPIRE].

  23. R.K. Kaul, Quantum phase transitions in bilayer SU(N) antiferromagnets, Phys. Rev. B 85 (2012) 180411.

  24. S.R. Coleman, J. Wess and B. Zumino, Structure of phenomenological Lagrangians. 1., Phys. Rev. 177 (1969) 2239 [INSPIRE].

  25. C.G. Callan Jr., S.R. Coleman, J. Wess and B. Zumino, Structure of phenomenological Lagrangians. 2., Phys. Rev. 177 (1969) 2247 [INSPIRE].

  26. A.P. Polychronakos, Physics and Mathematics of Calogero particles, J. Phys. A 39 (2006) 12793 [hep-th/0607033] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  27. S. Weinberg, Phenomenological Lagrangians, Physica A 96 (1979) 327 [INSPIRE].

  28. V. Arnold and B. Khesin, Topological Methods in Hydrodynamics, Applied Mathematical Sciences, Springer, New York U.S.A. (1999), https://books.google.ch/books?id=9Iwrt0l0nFMC.

  29. A. Monin, Partition function on spheres: How to use zeta function regularization, Phys. Rev. D 94 (2016) 085013 [arXiv:1607.06493] [INSPIRE].

  30. A. Nicolis, R. Penco and R.A. Rosen, Relativistic Fluids, Superfluids, Solids and Supersolids from a Coset Construction, Phys. Rev. D 89 (2014) 045002 [arXiv:1307.0517] [INSPIRE].

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Correspondence to Domenico Orlando.

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ArXiv ePrint: 1707.00710

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Loukas, O., Orlando, D. & Reffert, S. Matrix models at large charge. J. High Energ. Phys. 2017, 85 (2017). https://doi.org/10.1007/JHEP10(2017)085

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Keywords

  • Conformal Field Theory
  • Field Theories in Lower Dimensions