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On Newton-Cartan local renormalization group and anomalies

  • Regular Article - Theoretical Physics
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  • Published: 28 November 2016
  • Volume 2016, article number 163 (2016)
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On Newton-Cartan local renormalization group and anomalies
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  • Roberto Auzzi1,2,
  • Stefano Baiguera1,
  • Francesco Filippini1 &
  • …
  • Giuseppe Nardelli1,3 
  • 726 Accesses

  • 18 Citations

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A preprint version of the article is available at arXiv.

Abstract

Weyl consistency conditions are a powerful tool to study the irreversibility properties of the renormalization group. We apply this formalism to non-relativistic theories in 2 spatial dimensions with boost invariance and dynamical exponent z = 2. Different possibilities are explored, depending on the structure of the gravitational background used as a source for the energy-momentum tensor.

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References

  1. M.J. Duff, Twenty years of the Weyl anomaly, Class. Quant. Grav. 11 (1994) 1387 [hep-th/9308075] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. A.B. Zamolodchikov, Irreversibility of the Flux of the Renormalization Group in a 2D Field Theory, JETP Lett. 43 (1986) 730 [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  3. J.L. Cardy, Is There a c Theorem in Four-Dimensions?, Phys. Lett. B 215 (1988) 749 [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  4. H. Osborn, Derivation of a Four-dimensional c Theorem, Phys. Lett. B 222 (1989) 97 [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  5. I. Jack and H. Osborn, Analogs for the c Theorem for Four-dimensional Renormalizable Field Theories, Nucl. Phys. B 343 (1990) 647 [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  6. H. Osborn, Weyl consistency conditions and a local renormalization group equation for general renormalizable field theories, Nucl. Phys. B 363 (1991) 486 [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  7. Z. Komargodski and A. Schwimmer, On Renormalization Group Flows in Four Dimensions, JHEP 12 (2011) 099 [arXiv:1107.3987] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  8. Z. Komargodski, The Constraints of Conformal Symmetry on RG Flows, JHEP 07 (2012) 069 [arXiv:1112.4538] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  9. L. Bonora, P. Cotta-Ramusino and C. Reina, Conformal Anomaly and Cohomology, Phys. Lett. B 126 (1983) 305 [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  10. L. Bonora, P. Pasti and M. Bregola, Weyl Cocycles, Class. Quant. Grav. 3 (1986) 635 [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. J.-F. Fortin, B. Grinstein and A. Stergiou, Limit Cycles and Conformal Invariance, JHEP 01 (2013) 184 [arXiv:1208.3674] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. M.A. Luty, J. Polchinski and R. Rattazzi, The a-theorem and the Asymptotics of 4D Quantum Field Theory, JHEP 01 (2013) 152 [arXiv:1204.5221] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. I. Jack and H. Osborn, Constraints on RG Flow for Four Dimensional Quantum Field Theories, Nucl. Phys. B 883 (2014) 425 [arXiv:1312.0428] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  14. F. Baume, B. Keren-Zur, R. Rattazzi and L. Vitale, The local Callan-Symanzik equation: structure and applications, JHEP 08 (2014) 152 [arXiv:1401.5983] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  15. Y. Nakayama, Consistency of local renormalization group in D = 3, Nucl. Phys. B 879 (2014) 37 [arXiv:1307.8048] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. A. Stergiou, D. Stone and L.G. Vitale, Constraints on Perturbative RG Flows in Six Dimensions, JHEP 08 (2016) 010 [arXiv:1604.01782] [INSPIRE].

    Article  ADS  Google Scholar 

  17. R. Auzzi and B. Keren-Zur, Superspace formulation of the local RG equation, JHEP 05 (2015) 150 [arXiv:1502.05962] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  18. J. Gomis, P.-S. Hsin, Z. Komargodski, A. Schwimmer, N. Seiberg and S. Theisen, Anomalies, Conformal Manifolds and Spheres, JHEP 03 (2016) 022 [arXiv:1509.08511] [INSPIRE].

    Article  ADS  Google Scholar 

  19. Y. Nakayama, Scale invariance vs conformal invariance, Phys. Rept. 569 (2015) 1 [arXiv:1302.0884] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  20. G.M. Shore, The c and a-theorems and the Local Renormalisation Group, arXiv:1601.06662 [INSPIRE].

  21. D. Anselmi, D.Z. Freedman, M.T. Grisaru and A.A. Johansen, Nonperturbative formulas for central functions of supersymmetric gauge theories, Nucl. Phys. B 526 (1998) 543 [hep-th/9708042] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  22. D. Anselmi, Anomalies, unitarity and quantum irreversibility, Annals Phys. 276 (1999) 361 [hep-th/9903059] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  23. D. Anselmi, Inequalities for trace anomalies, length of the RG flow, distance between the fixed points and irreversibility, Class. Quant. Grav. 21 (2004) 29 [hep-th/0210124] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  24. I. Adam, I.V. Melnikov and S. Theisen, A Non-Relativistic Weyl Anomaly, JHEP 09 (2009) 130 [arXiv:0907.2156] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  25. M. Baggio, J. de Boer and K. Holsheimer, Anomalous Breaking of Anisotropic Scaling Symmetry in the Quantum Lifshitz Model, JHEP 07 (2012) 099 [arXiv:1112.6416] [INSPIRE].

    Article  ADS  Google Scholar 

  26. T. Griffin, P. Hořava and C.M. Melby-Thompson, Conformal Lifshitz Gravity from Holography, JHEP 05 (2012) 010 [arXiv:1112.5660] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  27. I. Arav, S. Chapman and Y. Oz, Lifshitz Scale Anomalies, JHEP 02 (2015) 078 [arXiv:1410.5831] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  28. I. Arav, S. Chapman and Y. Oz, Non-Relativistic Scale Anomalies, JHEP 06 (2016) 158 [arXiv:1601.06795] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  29. S. Pal and B. Grinstein, Weyl Consistency Conditions in Non-Relativistic Quantum Field Theory, arXiv:1605.02748 [INSPIRE].

  30. S. Deser and A. Schwimmer, Geometric classification of conformal anomalies in arbitrary dimensions, Phys. Lett. B 309 (1993) 279 [hep-th/9302047] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  31. K. Jensen, Anomalies for Galilean fields, arXiv:1412.7750 [INSPIRE].

  32. R. Auzzi and G. Nardelli, Heat kernel for Newton-Cartan trace anomalies, JHEP 07 (2016) 047 [arXiv:1605.08684] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  33. R. Auzzi, S. Baiguera and G. Nardelli, On Newton-Cartan trace anomalies, JHEP 02 (2016) 003 [Erratum ibid. 1602 (2016) 177] [arXiv:1511.08150] [INSPIRE].

  34. D.T. Son and M. Wingate, General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas, Annals Phys. 321 (2006) 197 [cond-mat/0509786] [INSPIRE].

  35. C. Hoyos and D.T. Son, Hall Viscosity and Electromagnetic Response, Phys. Rev. Lett. 108 (2012) 066805 [arXiv:1109.2651] [INSPIRE].

    Article  ADS  Google Scholar 

  36. D.T. Son, Newton-Cartan Geometry and the Quantum Hall Effect, arXiv:1306.0638 [INSPIRE].

  37. M. Geracie, D.T. Son, C. Wu and S.-F. Wu, Spacetime Symmetries of the Quantum Hall Effect, Phys. Rev. D 91 (2015) 045030 [arXiv:1407.1252] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  38. K. Jensen, On the coupling of Galilean-invariant field theories to curved spacetime, arXiv:1408.6855 [INSPIRE].

  39. J. Hartong, E. Kiritsis and N.A. Obers, Schrödinger Invariance from Lifshitz Isometries in Holography and Field Theory, Phys. Rev. D 92 (2015) 066003 [arXiv:1409.1522] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  40. J. Hartong, E. Kiritsis and N.A. Obers, Lifshitz space-times for Schrödinger holography, Phys. Lett. B 746 (2015) 318 [arXiv:1409.1519] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  41. J. Hartong, E. Kiritsis and N.A. Obers, Field Theory on Newton-Cartan Backgrounds and Symmetries of the Lifshitz Vacuum, JHEP 08 (2015) 006 [arXiv:1502.00228] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  42. C. Duval, G. Burdet, H.P. Kunzle and M. Perrin, Bargmann Structures and Newton-cartan Theory, Phys. Rev. D 31 (1985) 1841 [INSPIRE].

    ADS  MathSciNet  Google Scholar 

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Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Authors and Affiliations

  1. Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore, Via Musei 41, 25121, Brescia, Italy

    Roberto Auzzi, Stefano Baiguera, Francesco Filippini & Giuseppe Nardelli

  2. INFN Sezione di Perugia, Via A. Pascoli, 06123, Perugia, Italy

    Roberto Auzzi

  3. TIFPA - INFN, c/o Dipartimento di Fisica, Università di Trento, 38123, Povo, (TN), Italy

    Giuseppe Nardelli

Authors
  1. Roberto Auzzi
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  2. Stefano Baiguera
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  3. Francesco Filippini
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Corresponding author

Correspondence to Roberto Auzzi.

Additional information

ArXiv ePrint: 1610.00123

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Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

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Cite this article

Auzzi, R., Baiguera, S., Filippini, F. et al. On Newton-Cartan local renormalization group and anomalies. J. High Energ. Phys. 2016, 163 (2016). https://doi.org/10.1007/JHEP11(2016)163

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  • Received: 10 October 2016

  • Accepted: 21 November 2016

  • Published: 28 November 2016

  • DOI: https://doi.org/10.1007/JHEP11(2016)163

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Keywords

  • Anomalies in Field and String Theories
  • Renormalization Group
  • Space-Time Symmetries

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