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One loop partition function for topologically massive higher spin gravity

Abstract

We calculate the one loop partition function for topologically massive higher spin gravity (TMHSG) for arbitrary spin by taking the spin-3 TMHSG action constructed in arXiv:1107.0915 and subsequently generalising it for an arbitrary spin. We find that the final result can be put into a product form which cannot be holomorphically factorised. This is consistent with the expectation of a logarithmic CFT dual for TMHSG with boundary conditions that retain all normalisable modes in the bulk.

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References

  1. [1]

    S. Deser, R. Jackiw and S. Templeton, Topologically massive gauge theories, Annals Phys. 140 (1982) 372 [Erratum ibid. 185 (1988) 406] [Annals Phys. 185 (1988) 406] [Annals Phys. 281 (2000) 409] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  2. [2]

    S. Deser, R. Jackiw and S. Templeton, Three-dimensional massive gauge theories, Phys. Rev. Lett. 48 (1982) 975 [INSPIRE].

    Article  ADS  Google Scholar 

  3. [3]

    E. Witten, Three-dimensional gravity revisited, arXiv:0706.3359 [INSPIRE].

  4. [4]

    A. Maloney and E. Witten, Quantum gravity partition functions in three dimensions, JHEP 02 (2010) 029 [arXiv:0712.0155] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  5. [5]

    M.R. Gaberdiel, Constraints on extremal self-dual CFTs, JHEP 11 (2007) 087 [arXiv:0707.4073] [INSPIRE].

    ADS  Google Scholar 

  6. [6]

    M.R. Gaberdiel and C.A. Keller, Modular differential equations and null vectors, JHEP 09 (2008) 079 [arXiv:0804.0489] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  7. [7]

    W. Li, W. Song and A. Strominger, Chiral gravity in three dimensions, JHEP 04 (2008) 082 [arXiv:0801.4566] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  8. [8]

    J. Brown and M. Henneaux, Central charges in the canonical realization of asymptotic symmetries: an example from three-dimensional gravity, Commun. Math. Phys. 104 (1986) 207 [INSPIRE].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  9. [9]

    S.N. Solodukhin, Holography with gravitational Chern-Simons, Phys. Rev. D 74 (2006) 024015 [hep-th/0509148] [INSPIRE].

    ADS  Google Scholar 

  10. [10]

    P. Kraus and F. Larsen, Holographic gravitational anomalies, JHEP 01 (2006) 022 [hep-th/0508218] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  11. [11]

    S. Carlip, S. Deser, A. Waldron and D. Wise, Cosmological topologically massive gravitons and photons, Class. Quant. Grav. 26 (2009) 075008 [arXiv:0803.3998] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  12. [12]

    W. Li, W. Song and A. Strominger, Comment onCosmological Topological Massive Gravitons and Photons’, arXiv:0805.3101 [INSPIRE].

  13. [13]

    D. Grumiller, R. Jackiw and N. Johansson, Canonical analysis of cosmological topologically massive gravity at the chiral point, arXiv:0806.4185 [INSPIRE].

  14. [14]

    S. Carlip, S. Deser, A. Waldron and D. Wise, Topologically massive AdS gravity, Phys. Lett. B 666 (2008) 272 [arXiv:0807.0486] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  15. [15]

    G. Giribet, M. Kleban and M. Porrati, Topologically massive gravity at the chiral point is not chiral, JHEP 10 (2008) 045 [arXiv:0807.4703] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  16. [16]

    A. Strominger, A simple proof of the chiral gravity conjecture, arXiv:0808.0506 [INSPIRE].

  17. [17]

    D. Grumiller and N. Johansson, Instability in cosmological topologically massive gravity at the chiral point, JHEP 07 (2008) 134 [arXiv:0805.2610] [INSPIRE].

    Article  ADS  Google Scholar 

  18. [18]

    D. Grumiller and N. Johansson, Consistent boundary conditions for cosmological topologically massive gravity at the chiral point, Int. J. Mod. Phys. D 17 (2009) 2367 [arXiv:0808.2575] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  19. [19]

    D. Grumiller and I. Sachs, AdS 3 /LCFT 2 → correlators in cosmological topologically massive gravity, JHEP 03 (2010) 012 [arXiv:0910.5241] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  20. [20]

    K. Skenderis, M. Taylor and B.C. van Rees, Topologically massive gravity and the AdS/CFT correspondence, JHEP 09 (2009) 045 [arXiv:0906.4926] [INSPIRE].

    Article  ADS  Google Scholar 

  21. [21]

    K. Skenderis, M. Taylor and B.C. van Rees, AdS boundary conditions and the topologically massive gravity/CFT correspondence, arXiv:0909.5617 [INSPIRE].

  22. [22]

    M.R. Gaberdiel, D. Grumiller and D. Vassilevich, Graviton 1-loop partition function for 3-dimensional massive gravity, JHEP 11 (2010) 094 [arXiv:1007.5189] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  23. [23]

    A. Maloney, W. Song and A. Strominger, Chiral gravity, log gravity and extremal CFT, Phys. Rev. D 81 (2010) 064007 [arXiv:0903.4573] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  24. [24]

    A. Campoleoni, S. Fredenhagen, S. Pfenninger and S. Theisen, Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields, JHEP 11 (2010) 007 [arXiv:1008.4744] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  25. [25]

    A. Campoleoni, S. Fredenhagen and S. Pfenninger, Asymptotic W-symmetries in three-dimensional higher-spin gauge theories, JHEP 09 (2011) 113 [arXiv:1107.0290] [INSPIRE].

    Article  ADS  Google Scholar 

  26. [26]

    M. Henneaux and S.-J. Rey, Nonlinear W as asymptotic symmetry of three-dimensional higher spin Anti-de Sitter gravity, JHEP 12 (2010) 007 [arXiv:1008.4579] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  27. [27]

    M.R. Gaberdiel, R. Gopakumar and A. Saha, Quantum W -symmetry in AdS 3, JHEP 02 (2011) 004 [arXiv:1009.6087] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  28. [28]

    J.R. David, M.R. Gaberdiel and R. Gopakumar, The heat kernel on AdS 3 and its applications, JHEP 04 (2010) 125 [arXiv:0911.5085] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  29. [29]

    M.R. Gaberdiel and R. Gopakumar, An AdS 3 dual for minimal model CFTs, Phys. Rev. D 83 (2011) 066007 [arXiv:1011.2986] [INSPIRE].

    ADS  Google Scholar 

  30. [30]

    A. Castro, A. Lepage-Jutier and A. Maloney, Higher spin theories in AdS 3 and a gravitational exclusion principle, JHEP 01 (2011) 142 [arXiv:1012.0598] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  31. [31]

    M.R. Gaberdiel and T. Hartman, Symmetries of holographic minimal models, JHEP 05 (2011) 031 [arXiv:1101.2910] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  32. [32]

    C. Ahn, The large-Nt Hooft limit of coset minimal models, JHEP 10 (2011) 125 [arXiv:1106.0351] [INSPIRE].

    Article  ADS  Google Scholar 

  33. [33]

    M.R. Gaberdiel, R. Gopakumar, T. Hartman and S. Raju, Partition functions of holographic minimal models, JHEP 08 (2011) 077 [arXiv:1106.1897] [INSPIRE].

    Article  ADS  Google Scholar 

  34. [34]

    M.R. Gaberdiel and C. Vollenweider, Minimal model holography for SO(2N), arXiv:1106.2634 [INSPIRE].

  35. [35]

    C.-M. Chang and X. Yin, Higher spin gravity with matter in AdS 3 and its CFT dual, arXiv:1106.2580 [INSPIRE].

  36. [36]

    A. Bagchi, S. Lal, A. Saha and B. Sahoo, Topologically massive higher spin gravity, JHEP 10 (2011) 150 [arXiv:1107.0915] [INSPIRE].

    Article  ADS  Google Scholar 

  37. [37]

    B. Chen, J. Long and J.-b. Wu, Spin-3 topological massive gravity, Phys. Lett. B 705 (2011) 513 [arXiv:1106.5141] [INSPIRE].

    ADS  Google Scholar 

  38. [38]

    R. Camporesi and A. Higuchi, Spectral functions and zeta functions in hyperbolic spaces, J. Math. Phys. 35 (1994) 4217 [INSPIRE].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  39. [39]

    A. Castro, T. Hartman and A. Maloney, The gravitational exclusion principle and null states in Anti-de Sitter space, Class. Quant. Grav. 28 (2011) 195012 [arXiv:1107.5098] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  40. [40]

    A. Zamolodchikov, Infinite additional symmetries in two-dimensional conformal quantum field theory, Theor. Math. Phys. 65 (1985) 1205 [INSPIRE].

    Article  MathSciNet  Google Scholar 

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Correspondence to Bindusar Sahoo.

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ArXiv ePrint: 1107.2063

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Bagchi, A., Lal, S., Saha, A. et al. One loop partition function for topologically massive higher spin gravity. J. High Energ. Phys. 2011, 68 (2011). https://doi.org/10.1007/JHEP12(2011)068

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Keywords

  • Gauge-gravity correspondence
  • AdS-CFT Correspondence
  • Conformal and W Symmetry