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Anomalous breaking of anisotropic scaling symmetry in the quantum lifshitz model

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Abstract

In this note we investigate the anomalous breaking of anisotropic scaling symmetry (t, x) → (λz t, λ x) in a non-relativistic field theory with dynamical exponent z = 2. On general grounds, one can show that there exist two possible “central charges” which characterize the breaking of scale invariance. Using heat kernel methods, we compute these two central charges in the quantum Lifshitz model, a free field theory which is second order in time and fourth order in spatial derivatives. We find that one of the two central charges vanishes. Interestingly, this is also true for strongly coupled non-relativistic field theories with a geometric dual described by a metric and a massive vector field.

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References

  1. D. Son, Toward an AdS/cold atoms correspondence: A Geometric realization of the Schrödinger symmetry, Phys. Rev. D 78 (2008) 046003 [arXiv:0804.3972] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  2. K. Balasubramanian and J. McGreevy, Gravity duals for non-relativistic CFTs, Phys. Rev. Lett. 101 (2008) 061601 [arXiv:0804.4053] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  3. S. Kachru, X. Liu and M. Mulligan, Gravity Duals of Lifshitz-like Fixed Points, Phys. Rev. D 78 (2008) 106005 [arXiv:0808.1725] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  4. P. Koroteev and M. Libanov, On existence of self-tuning solutions in static braneworlds without singularities, JHEP 02 (2008) 104 [arXiv:0712.1136].

    Article  MathSciNet  ADS  Google Scholar 

  5. M. Guica, K. Skenderis, M. Taylor and B.C. van Rees, Holography for Schrödinger backgrounds, JHEP 02 (2011) 056 [arXiv:1008.1991].

    Article  ADS  Google Scholar 

  6. S.F. Ross, Holography for asymptotically locally Lifshitz spacetimes, Class. Quant. Grav. 28 (2011) 215019 [arXiv:1107.4451].

    Article  ADS  Google Scholar 

  7. M. Baggio, J. de Boer and K. Holsheimer, Hamilton-Jacobi renormalization for Lifshitz spacetime, JHEP 01 (2012) 058 [arXiv:1107.5562].

    Article  ADS  Google Scholar 

  8. R.B. Mann and R. McNees, Holographic renormalization for asymptotically Lifshitz spacetimes, JHEP 10 (2011) 129 [arXiv:1107.5792].

    Article  MathSciNet  ADS  Google Scholar 

  9. M. Henningson and K. Skenderis, The holographic Weyl anomaly, JHEP 07 (1998) 023 [hep-th/9806087].

    Article  MathSciNet  ADS  Google Scholar 

  10. I. Adam, I.V. Melnikov and S. Theisen, A non-relativistic Weyl anomaly, JHEP 09 (2009) 130 [arXiv:0907.2156].

    Article  MathSciNet  ADS  Google Scholar 

  11. P.R.S. Gomes and M. Gomes, Ward identities in Lifshitz-like field theories, Phys. Rev. D 85 (2012) 065010 [arXiv:1112.3887].

    ADS  Google Scholar 

  12. E. Ardonne, P. Fendley and E. Fradkin, Topological order and conformal quantum critical points, Ann. Phys. 310 (2004) 493 [cond-mat/0311466].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. T. Griffin, P. Hořava and C.M. Melby-Thompson, Conformal Lifshitz gravity from holography, JHEP 05 (2012) 010 [arXiv:1112.5660].

    Article  ADS  Google Scholar 

  14. G. Grinstein, Anisotropic sine-gordon model and infinite-order phase transitions in three dimensions, Phys. Rev. B 23 (1981) 4615.

    MathSciNet  ADS  Google Scholar 

  15. P. Di Francesco, P. Mathieu and D. Senechal, Conformal field theory (1997).

  16. D.V. Vassilevich, Heat kernel expansion: user’s manual, Phys. Rept. 388 (2003) 279 [hep-th/0306138].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. A. Ceresole, P. Pizzochero and P. van Nieuwenhuizen, The curved space trace, chiral and einstein anomalies from path integrals, using flat space plane waves, Phys. Rev. D 39 (1989) 1567.

    ADS  Google Scholar 

  18. J. de Boer, E. Verlinde and H. Verlinde, On the holographic renormalization group, JHEP 08 (2000) 003 [hep-th/9912012].

    Article  Google Scholar 

  19. D. Martelli and W. Mück, Holographic renormalization and Ward identities with the Hamilton-Jacobi method, Nucl. Phys. B 654 (2003) 248 [hep-th/0205061].

    Article  ADS  Google Scholar 

  20. S.F. Ross and O. Saremi, Holographic stress tensor for non-relativistic theories, JHEP 09 (2009) 009 [arXiv:0907.1846].

    Article  MathSciNet  ADS  Google Scholar 

  21. A. Adams, A. Maloney, A. Sinha and S.E. Vázquez, 1/N effects in non-relativistic gauge-gravity duality, JHEP 03 (2009) 097 [arXiv:0812.0166].

    Article  ADS  Google Scholar 

  22. P.B. Gilkey, The spectral geometry of the higher order laplacian, Duke Math. J. 47 (1980) 511.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Institute for Theoretical Physics, University of Amsterdam, Science Park 904, Postbus 94485, 1090 GL, Amsterdam, The Netherlands

    Marco Baggio, Jan de Boer & Kristian Holsheimer

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  1. Marco Baggio
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  2. Jan de Boer
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  3. Kristian Holsheimer
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Correspondence to Kristian Holsheimer.

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ArXiv ePrint: 1112.6416

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Baggio, M., de Boer, J. & Holsheimer, K. Anomalous breaking of anisotropic scaling symmetry in the quantum lifshitz model. J. High Energ. Phys. 2012, 99 (2012). https://doi.org/10.1007/JHEP07(2012)099

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  • DOI: https://doi.org/10.1007/JHEP07(2012)099

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