×

Chiral description of massive gravity. (English) Zbl 1342.83043

Summary: We propose and study a new first order version of the ghost-free massive gravity. Instead of metrics or tetrads, it uses a connection together with Plebanski’s chiral 2-forms as fundamental variables, rendering the phase space structure similar to that of \(\mathrm{SU}(2)\) gauge theories. The chiral description simplifies computations of the constraint algebra, and allows us to perform the complete canonical analysis of the system. In particular, we explicitly compute the secondary constraint and carry out the stabilization procedure, thus proving that in general the theory propagates 7 degrees of freedom, consistently with previous claims. Finally, we point out that the description in terms of 2-forms opens the door to an infinite class of ghost-free massive bi-gravity actions. Our results apply directly to Euclidean signature. The reality conditions to be imposed in the Lorentzian signature appear to be more complicated than in the usual gravity case and are left as an open issue.

MSC:

83C20 Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] K. Hinterbichler, Theoretical aspects of massive gravity, Rev. Mod. Phys. 84 (2012) 671 [arXiv:1105.3735] [INSPIRE]. · doi:10.1103/RevModPhys.84.671
[2] D. Boulware and S. Deser, Can gravitation have a finite range?, Phys. Rev. D 6 (1972) 3368 [INSPIRE].
[3] C. Deffayet and J.-W. Rombouts, Ghosts, strong coupling and accidental symmetries in massive gravity, Phys. Rev. D 72 (2005) 044003 [gr-qc/0505134] [INSPIRE].
[4] A. Vainshtein, To the problem of nonvanishing gravitation mass, Phys. Lett. B 39 (1972) 393 [INSPIRE].
[5] H. van Dam and M. Veltman, Massive and massless Yang-Mills and gravitational fields, Nucl. Phys. B 22 (1970) 397 [INSPIRE].
[6] N. Arkani-Hamed, H. Georgi and M.D. Schwartz, Effective field theory for massive gravitons and gravity in theory space, Annals Phys. 305 (2003) 96 [hep-th/0210184] [INSPIRE]. · Zbl 1022.81035 · doi:10.1016/S0003-4916(03)00068-X
[7] C. de Rham and G. Gabadadze, Generalization of the Fierz-Pauli Action, Phys. Rev. D 82 (2010) 044020 [arXiv:1007.0443] [INSPIRE].
[8] C. de Rham, G. Gabadadze and A.J. Tolley, Resummation of massive gravity, Phys. Rev. Lett. 106 (2011) 231101 [arXiv:1011.1232] [INSPIRE]. · doi:10.1103/PhysRevLett.106.231101
[9] C. de Rham, G. Gabadadze and A.J. Tolley, Ghost free massive gravity in the Stückelberg language, Phys. Lett. B 711 (2012) 190 [arXiv:1107.3820] [INSPIRE].
[10] C. Burrage, N. Kaloper and A. Padilla, Strong coupling and bounds on the graviton mass in massive gravity, arXiv:1211.6001 [INSPIRE].
[11] S. Hassan and R.A. Rosen, Resolving the ghost problem in non-linear massive gravity, Phys. Rev. Lett. 108 (2012) 041101 [arXiv:1106.3344] [INSPIRE]. · doi:10.1103/PhysRevLett.108.041101
[12] S. Hassan, R.A. Rosen and A. Schmidt-May, Ghost-free massive gravity with a general reference metric, JHEP02 (2012) 026 [arXiv:1109.3230] [INSPIRE]. · Zbl 1309.83084 · doi:10.1007/JHEP02(2012)026
[13] S. Hassan and R.A. Rosen, Bimetric gravity from ghost-free massive gravity, JHEP02 (2012) 126 [arXiv:1109.3515] [INSPIRE]. · Zbl 1309.83083 · doi:10.1007/JHEP02(2012)126
[14] S. Hassan and R.A. Rosen, Confirmation of the secondary constraint and absence of ghost in massive gravity and bimetric gravity, JHEP04 (2012) 123 [arXiv:1111.2070] [INSPIRE]. · Zbl 1348.83065 · doi:10.1007/JHEP04(2012)123
[15] L. Alberte, A.H. Chamseddine and V. Mukhanov, Massive gravity: exorcising the ghost, JHEP04 (2011) 004 [arXiv:1011.0183] [INSPIRE]. · Zbl 1250.81130 · doi:10.1007/JHEP04(2011)004
[16] A.H. Chamseddine and V. Mukhanov, Massive gravity simplified: a quadratic action, JHEP08 (2011) 091 [arXiv:1106.5868] [INSPIRE]. · Zbl 1298.83106 · doi:10.1007/JHEP08(2011)091
[17] J. Kluson, Note about hamiltonian structure of non-linear massive gravity, JHEP01 (2012) 013 [arXiv:1109.3052] [INSPIRE]. · Zbl 1306.83064 · doi:10.1007/JHEP01(2012)013
[18] D. Comelli, M. Crisostomi, F. Nesti and L. Pilo, Spherically symmetric solutions in ghost-free massive gravity, Phys. Rev. D 85 (2012) 024044 [arXiv:1110.4967] [INSPIRE]. · Zbl 1309.83030
[19] A. Golovnev, On the hamiltonian analysis of non-linear massive gravity, Phys. Lett. B 707 (2012) 404 [arXiv:1112.2134] [INSPIRE].
[20] J. Kluson, Comments about hamiltonian formulation of non-linear massive gravity with Stückelberg fields, JHEP06 (2012) 170 [arXiv:1112.5267] [INSPIRE]. · Zbl 1397.83015 · doi:10.1007/JHEP06(2012)170
[21] I. Buchbinder, D. Pereira and I. Shapiro, One-loop divergences in massive gravity theory, Phys. Lett. B 712 (2012) 104 [arXiv:1201.3145] [INSPIRE].
[22] J. Kluson, Remark about hamiltonian formulation of non-linear massive gravity in Stückelberg formalism, Phys. Rev. D 86 (2012) 124005 [arXiv:1202.5899] [INSPIRE].
[23] J. Kluson, Non-linear massive gravity with additional primary constraint and absence of ghosts, Phys. Rev. D 86 (2012) 044024 [arXiv:1204.2957] [INSPIRE].
[24] S. Hassan, A. Schmidt-May and M. von Strauss, Metric formulation of ghost-free multivielbein theory, arXiv:1204.5202 [INSPIRE].
[25] S. Hassan, A. Schmidt-May and M. von Strauss, On consistent theories of massive spin-2 fields coupled to gravity, JHEP05 (2013) 086 [arXiv:1208.1515] [INSPIRE]. · Zbl 1342.83534 · doi:10.1007/JHEP05(2013)086
[26] J. Kluson, Note about hamiltonian formalism for general non-linear massive gravity action in Stückelberg formalism, arXiv:1209.3612 [INSPIRE]. · Zbl 1280.83002
[27] K. Hinterbichler and R.A. Rosen, Interacting spin-2 fields, JHEP07 (2012) 047 [arXiv:1203.5783] [INSPIRE]. · doi:10.1007/JHEP07(2012)047
[28] C. Deffayet, J. Mourad and G. Zahariade, Covariant constraints in ghost free massive gravity, JCAP01 (2013) 032 [arXiv:1207.6338] [INSPIRE]. · doi:10.1088/1475-7516/2013/01/032
[29] C. Deffayet, J. Mourad and G. Zahariade, A note on ’symmetric’ vielbeins in bimetric, massive, perturbative and non perturbative gravities, JHEP03 (2013) 086 [arXiv:1208.4493] [INSPIRE]. · Zbl 1342.83067 · doi:10.1007/JHEP03(2013)086
[30] S. Hassan, A. Schmidt-May and M. von Strauss, Proof of consistency of nonlinear massive gravity in the Stückelberg formulation, Phys. Lett. B 715 (2012) 335 [arXiv:1203.5283] [INSPIRE].
[31] J.F. Plebanski, On the separation of Einsteinian substructures, J. Math. Phys.18 (1977) 2511 [INSPIRE]. · Zbl 0368.53032 · doi:10.1063/1.523215
[32] R. Capovilla, T. Jacobson, J. Dell and L. Mason, Selfdual two forms and gravity, Class. Quant. Grav. 8 (1991) 41 [INSPIRE]. · Zbl 0716.53066 · doi:10.1088/0264-9381/8/1/009
[33] K. Krasnov, Plebanski formulation of general relativity: a practical introduction, Gen. Rel. Grav. 43 (2011) 1 [arXiv:0904.0423] [INSPIRE]. · Zbl 1208.83001 · doi:10.1007/s10714-010-1061-x
[34] H. Urbantke, On integrability properties of SU(2) Yang-Mills fields. I. Infinitesimal part, J. Math. Phys.25 (1984) 2321 [INSPIRE]. · doi:10.1063/1.526402
[35] K. Krasnov, Plebanski gravity without the simplicity constraints, Class. Quant. Grav. 26 (2009) 055002 [arXiv:0811.3147] [INSPIRE]. · Zbl 1160.83305 · doi:10.1088/0264-9381/26/5/055002
[36] A. Ashtekar, Lectures on nonperturbative canonical gravity, Adv. Ser. Astrophys. Cosmol.6 (1991) 1 [INSPIRE].
[37] T. Thiemann, Modern canonical quantum general relativity, gr-qc/0110034 [INSPIRE]. · Zbl 1129.83004
[38] S. Hojman, K. Kuchar and C. Teitelboim, Geometrodynamics regained, Annals Phys. 96 (1976) 88 [INSPIRE]. · Zbl 0318.53033 · doi:10.1016/0003-4916(76)90112-3
[39] S.Y. Alexandrov and D. Vassilevich, Path integral for the Hilbert-Palatini and Ashtekar gravity, Phys. Rev. D 58 (1998) 124029 [gr-qc/9806001] [INSPIRE].
[40] T. Damour and I.I. Kogan, Effective lagrangians and universality classes of nonlinear bigravity, Phys. Rev. D 66 (2002) 104024 [hep-th/0206042] [INSPIRE].
[41] J. Kluson, Hamiltonian formalism of particular bimetric gravity model, arXiv:1211.6267 [INSPIRE]. · Zbl 1290.83022
[42] S. Alexandrov, Degenerate Plebanski sector and spin foam quantization, Class. Quant. Grav. 29 (2012) 145018 [arXiv:1202.5039] [INSPIRE]. · Zbl 1248.83025 · doi:10.1088/0264-9381/29/14/145018
[43] K. Krasnov, On deformations of Ashtekar’s constraint algebra, Phys. Rev. Lett. 100 (2008) 081102 [arXiv:0711.0090] [INSPIRE]. · Zbl 1228.83019 · doi:10.1103/PhysRevLett.100.081102
[44] K. Krasnov, Effective metric lagrangians from an underlying theory with two propagating degrees of freedom, Phys. Rev. D 81 (2010) 084026 [arXiv:0911.4903] [INSPIRE].
[45] D. Comelli, M. Crisostomi, F. Nesti and L. Pilo, Degrees of freedom in massive gravity, Phys. Rev. D 86 (2012) 101502 [arXiv:1204.1027] [INSPIRE]. · Zbl 1309.83030
[46] S. Dubovsky, Phases of massive gravity, JHEP10 (2004) 076 [hep-th/0409124] [INSPIRE]. · doi:10.1088/1126-6708/2004/10/076
[47] M.P. Reisenberger, Classical Euclidean general relativity from ’left-handed area = right-handed area’, gr-qc/9804061 [INSPIRE]. · Zbl 0964.83006
[48] R. De Pietri and L. Freidel, SO(4) Plebanski action and relativistic spin foam model, Class. Quant. Grav. 16 (1999) 2187 [gr-qc/9804071] [INSPIRE]. · Zbl 0942.83050 · doi:10.1088/0264-9381/16/7/303
[49] A. Perez, Spin foam models for quantum gravity, Class. Quant. Grav.20 (2003) R43 [gr-qc/0301113] [INSPIRE]. · Zbl 1030.83002 · doi:10.1088/0264-9381/20/6/202
[50] S. Alexandrov, M. Geiller and K. Noui, Spin foams and canonical quantization, SIGMA8 (2012) 055 [arXiv:1112.1961] [INSPIRE]. · Zbl 1270.83018
[51] E. Buffenoir, M. Henneaux, K. Noui and P. Roche, Hamiltonian analysis of Plebanski theory, Class. Quant. Grav. 21 (2004) 5203 [gr-qc/0404041] [INSPIRE]. · Zbl 1062.83005 · doi:10.1088/0264-9381/21/22/012
[52] S. Alexandrov, E. Buffenoir and P. Roche, Plebanski theory and covariant canonical formulation, Class. Quant. Grav. 24 (2007) 2809 [gr-qc/0612071] [INSPIRE]. · Zbl 1117.83057 · doi:10.1088/0264-9381/24/11/003
[53] S. Alexandrov and K. Krasnov, Hamiltonian analysis of non-chiral Plebanski theory and its generalizations, Class. Quant. Grav. 26 (2009) 055005 [arXiv:0809.4763] [INSPIRE]. · Zbl 1160.83301 · doi:10.1088/0264-9381/26/5/055005
[54] S. Speziale, Bi-metric theory of gravity from the non-chiral Plebanski action, Phys. Rev. D 82 (2010) 064003 [arXiv:1003.4701] [INSPIRE].
[55] D. Beke, G. Palmisano and S. Speziale, Pauli-Fierz Mass Term in Modified Plebanski Gravity, JHEP03 (2012) 069 [arXiv:1112.4051] [INSPIRE]. · Zbl 1309.83045 · doi:10.1007/JHEP03(2012)069
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.