Geometric flows in Hořava-Lifshitz gravity

Journal of High Energy Physics

Volumn 2010, Issue 4, 2010, Pages

  Bakas, Ioannis ^a   Bourliot, François ^b   Lüst, Dieter ^c,d   Petropoulos, Marios ^b  

^a UNIVERSITY OF PATRAS   (Greece)

^b CENTRE DE PHYSIQUE THÉORIQUE   (France)

^c MAX PLANCK INSTITUT FÜR PHYSIK   (Germany)

^d UNIVERSITY OF MUNICH   (Germany)

Author keywords

Classical theories of gravity; Differential and algebraic geometry; Solitons monopoles and instantons

Indexed keywords

EID: 77954928745     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP04(2010)131     Document Type: Article

References (70)

1. E.M. Lifshitz, On the theory of second order phase transitions I & II, Zh. Eksp. Teor. Fiz. 11 (1941) 255 & 269.
2. S. Chadha and H.B. Nielsen, Lorentz invariance as a low-energy phenomenon, Nucl. Phys. B 217 (1983) 125 [SPIRES].
3. J. Iliopoulos, D.V. Nanopoulos and T.N. Tomaras, Infrared stability or anti grand unifcation , Phys. Lett. B 94 (1980) 141 [SPIRES].
4. I. Antoniadis, J. Iliopoulos and T. Tomaras, On the infrared stability of gauge theories, Nucl. Phys. B 227 (1983) 447 [SPIRES].
5. M. Petrini, Infrared stability of N = 4 super Yang-Mills theory, Phys. Lett. B 404 (1997) 66 [hep-th/9704004] [SPIRES].
6. P. Hořava , Membranes at Quantum Criticality, JHEP 03 (2009) 020 [arXiv:0812.4287] [SPIRES].
7. P. Hořava, Quantum Gravity at a Lifshitz Point, Phys. Rev. D 79 (2009) 084008 [arXiv:0901.3775] [SPIRES].
8. D. Orlando and S. Reffert, On the Renormalizability of Hořava-Lifshitz-type Gravities, Class. Quant. Grav. 26 (2009) 155021 [arXiv:0905.0301] [SPIRES].
9. F.-W. Shu and Y.-S. Wu, Stochastic Quantization of the Hořava Gravity, arXiv:0906.1645 [SPIRES].
10. C. Charmousis, G. Niz, A. Padilla and P.M. Saffin, Strong coupling in Hořava gravity, JHEP 08 (2009) 070 [arXiv:0905.2579] [SPIRES].
11. M. Li and Y. Pang, A Trouble with Hořava-Lifshitz Gravity, JHEP 08 (2009) 015 [arXiv:0905.2751] [SPIRES].
12. D. Blas, O. Pujolàs and S. Sibiryakov, On the Extra Mode and Inconsistency of Hořava Gravity, JHEP 10 (2009) 029 [arXiv:0906.3046] [SPIRES].
13. D. Blas, O. Pujolàs and S. Sibiryakov, A healthy extension of Hořava gravity, arXiv:0909.3525 [SPIRES].
14. D. Blas, O. Pujolàs and S. Sibiryakov, Comment on 'Strong coupling in extended Hořava-Lifshitz gravity', arXiv:0912.0550 [SPIRES].
15. K. Koyama and F. Arroja, Pathological behaviour of the scalar graviton in Hořava-Lifshitz gravity, JHEP 03 (2010) 061 [arXiv:0910.1998] [SPIRES].
16. R. Hamilton, Three-manifolds with positive Ricci curvature, J. Diff. Geom. 17 (1982) 255.
17. G. Perelman, The entropy formula for the Ricci flow and its geometric applications, math/0211159 [SPIRES].
18. G. Perelman, Ricci flow with surgery on three-manifolds, math/0303109 [SPIRES].
19. G. Perelman, Finite extinction time for the solutions to the Ricci flow on certain three-manifolds, math/0307245 [SPIRES].
20. H.-D. Cao, B. Chow, S.-C. Chu and S.-T. Yau eds., Collected Papers on Ricci Flow, Series in Geometry and Topology, 37, International Press, Somerville U.S.A. (2003).
21. J.W. Morgan and G. Tian,Ricci Flow and the poincaré conjecture clay mathematics monographs , Amer. Math. Soc., Cambridge U.S.A. (2007) [math.DG/0607607].
22. D. Friedan, Nonlinear Models in Two Epsilon Dimensions, Phys. Rev. Lett. 45 (1980) 1057 [SPIRES].
23. D.H. Friedan, Nonlinear Models in Two + Epsilon Dimensions, Ann. Phys. 163 (1985) 318 [SPIRES].
24. C. Schmidhuber and A.A. Tseytlin, On string cosmology and the RG flow in 2-D field theory, Nucl. Phys. B 426 (1994) 187 [hep-th/9404180] [SPIRES].
25. I. Bakas, D. Orlando and P.M. Petropoulos, Ricci ows and expansion in axion-dilaton cosmology, JHEP 01 (2007) 040 [hep-th/0610281] [SPIRES].
26. M. Cvetič, G.W. Gibbons, H. Lü and C.N. Pope, Cohomogeneity one manifolds of Spin(7) and G2 holonomy, Phys. Rev. D 65 (2002) 106004 [hep-th/0108245] [SPIRES].
27. I. Bakas and K. Sfetsos, unpublished work (2004).
28. G.W. Gibbons, private communication (2005).
29. F. Bourliot, J. Estes, P.M. Petropoulos and P. Spindel, Gravitational instantons, self-duality and geometric ows, arXiv:0906.4558 [SPIRES].
30. J.B. Hartle and S.W. Hawking, Wave function of the universe, Phys. Rev. D28 (1983) 2960 [SPIRES].
31. C.W. Misner, Mixmaster universe, Phys. Rev. Lett. 22 (1969) 1071 [SPIRES].
32. C.W. Misner, Quantum cosmology. 1, Phys. Rev. 186 (1969) 1319 [SPIRES].
33. V.A. Belinsky, I.M. Khalatnikov and E.M. Lifshitz, Oscillatory approach to a singular point in the relativistic cosmology, Adv. Phys. 19 (1970) 525 [SPIRES].
34. V.A. Belinsky, I.M. Khalatnikov and E.M. Lifshitz, A General Solution of the Einstein Equations with a Time Singularity, Adv. Phys. 31 (1982) 639 [SPIRES].
35. J.D. Barrow, Chaotic behavior in general relativity, Phys. Rept. 85 (1982) 1 [SPIRES].
36. I. Bakas, F. Bourliot, D. Lüst and M. Petropoulos, Mixmaster universe in Hořava-Lifshitz gravity, Class. Quant. Grav. 27 (2010) 045013 [arXiv:0911.2665] [SPIRES].
37. Y.S. Myung, Y.-W. Kim, W.-S. Son and Y.-J. Park, Chaotic universe in the z = 2 Hovava-Lifshitz gravity, arXiv:0911.2525 [SPIRES].
38. L. Carroll, Alice's Adventures in Wonderland, MacMillan, London U.K. (1865).
39. C.W. Misner, K.S. Thorne and J.A. Wheeler, Gravitation, Freeman, San Francisco U.S.A. (1973).
40. M. Henneaux, A. Kleinschmidt and G.L. Gomez, A dynamical inconsistency of Hořava gravity, Phys. Rev. D 81 (2010) 064002 [arXiv:0912.0399] [SPIRES].
41. S. Deser, R. Jackiw and S. Templeton, Topologically massive gauge theories, Ann. Phys. 140 (1982) 372
42. [Erratum ibid. 185 (1988) 406] [SPIRES].
43. S. Deser, R. Jackiw and S. Templeton, Three-Dimensional Massive Gauge Theories, Phys. Rev. Lett. 48 (1982) 975 [SPIRES].
44. T. Eguchi, P.B. Gilkey and A.J. Hanson, Gravitation, Gauge Theories and Diferential Geometry, Phys. Rept. 66 (1980) 213 [SPIRES].
45. G.W. Gibbons and C.N. Pope, The Positive Action Conjecture and Asymptotically Euclidean Metrics in Quantum Gravity, Commun. Math. Phys. 66 (1979) 267 [SPIRES].
46. R.S. Hamilton, The Ricci ow on surfaces, in Mathematics and General Relativity, Contemp. Math. 71, Amer. Math. Soc., Providence U.S.A. (1988), pg. 237{262.
47. A.U.O. Kisisel, O. Sarioglu and B. Tekin, Cotton ow, Class. Quant. Grav. 25 (2008) 165019 [arXiv:0803.1603] [SPIRES].
48. J. Isenberg and M. Jackson, Ricci flow of locally homogeneous geometries on closed manifolds, J. Diff. Geom. 35 (1992) 723.
49. G. Darboux, Mémoire sur la théorie des coordonnées curvilignes et des systèmes orthogonaux, Ann. Ec. Normale Supér. 7 (1878) 101.
50. G.-H. Halphen, Sur un systèmes déquations diérentielles, C.R. Acad. Sc. Paris 92 (1881) 1001.
51. G.-H. Halphen, Sur certains systèmes déquations diérentielles, C.R. Acad. Sc. Paris 92 (1881) 1004.
52. L.A. Takhtajan, A Simple example of modular forms as tau functions for integrable equations, Theor. Math. Phys. 93 (1992) 1308 [SPIRES].
53. M.F. Atiyah and N.J. Hitchin, Low-Energy Scattering of Nonabelian Monopoles, Phys. Lett. A 107 (1985) 21 [SPIRES].
54. M.F. Atiyah and N.J. Hitchin, The Geometry and Dynamics of Magnetic Monopoles, Porter Lectures, Princeton University Press, Princeton U.S.A. (1988).
55. G.W. Gibbons and N.S. Manton, Classical and Quantum Dynamics of BPS Monopoles, Nucl. Phys. B 274 (1986) 183 [SPIRES].
56. Y. Nutku and P. Bakler, Homogeneous, anisotropic three manifolds of topologically massive gravity, Annals Phys. 195 (1989) 16 [SPIRES].
57. G. Calcagni, Cosmology of the Lifshitz universe, JHEP 09 (2009) 112 [arXiv:0904.0829] [SPIRES].
58. E. Kiritsis and G. Kofnas, Hořava-Lifshitz Cosmology, Nucl. Phys. B 821 (2009) 467 [arXiv:0904.1334] [SPIRES].
59. R. Brandenberger, Matter Bounce in Hořava-Lifshitz Cosmology, Phys. Rev. D 80 (2009) 043516 [arXiv:0904.2835] [SPIRES].
60. G.W. Gibbons and S.W. Hawking, Classiffcation of Gravitational Instanton Symmetries, Commun. Math. Phys. 66 (1979) 291 [SPIRES].
61. G.W. Gibbons, S.W. Hawking and M.J. Perry, Path Integrals and the Indefniteness of the Gravitational Action, Nucl. Phys. B 138 (1978) 141 [SPIRES].
62. A. Kehagias and K. Sfetsos, The black hole and FRW geometries of non-relativistic gravity, Phys. Lett. B 678 (2009) 123 [arXiv:0905.0477] [SPIRES].
63. H. Lü, J. Mei and C.N. Pope, Solutions to Hořava Gravity, Phys. Rev. Lett. 103 (2009) 091301 [arXiv:0904.1595] [SPIRES].
64. E. Kiritsis and G. Kofnas, On Hořava-Lifshitz "Black Holes", JHEP 01 (2010) 122 [arXiv:0910.5487] [SPIRES].
65. M. Gurses, Killing Vector Fields in Three Dimensions: A Method to Solve Massive Gravity Field Equations, arXiv:1001.1039 [SPIRES].
66. D.D.K. Chow, C.N. Pope and E. Sezgin, Classifcation of solutions in topologically massive gravity, arXiv:0906.3559 [SPIRES].
67. R. Bach, Zur Weylschen Relativitätstheorie und der Weylschen Erweiterung des Krümmungsbegriffs, Math. Zeitschr. 9 (1921) 110.
68. E. Calabi, Extremal Kähler metric, in Seminar on Differential Geometry, S.-T. Yau ed., Annals of Mathematical Studies 102, Princeton University Press, Princeton U.S.A (1982).
69. E.A. Bergshoeff, O. Hohm and P.K. Townsend, Massive Gravity in Three Dimensions, Phys. Rev. Lett. 102 (2009) 201301 [arXiv:0901.1766] [SPIRES].
70. I. Bakas and C. Sourdis, work in progress.