|
SIGMA 2 (2006), 020, 34 pages hep-th/0602145
https://doi.org/10.3842/SIGMA.2006.020
Duality-Symmetric Approach to General Relativity and Supergravity
Alexei J. Nurmagambetov
A.I. Akhiezer Institute for Theoretical Physics, NSC "Kharkov Institute of Physics and Technology", 1
Akademicheskaya Str., Kharkiv, 61108 Ukraine
Received October 19, 2005, in final form February 03, 2006; Published online February 15, 2006; Some references added and typos corrected March 10, 2006
Abstract
We review the application of a duality-symmetric
approach to gravity and supergravity with emphasizing benefits
and disadvantages of the formulation. Contents of these notes
includes: 1) Introduction with putting the accent on the role of
dual gravity within M-theory; 2) Dualization of gravity with a
cosmological constant in D = 3; 3) On-shell description of
dual gravity in D > 3; 4) Construction of the
duality-symmetric action for General Relativity with/without
matter fields; 5) On-shell description of dual gravity in
linearized approximation; 6) Brief summary of the paper.
Key words:
duality; gravity; supergravity.
pdf (464 kb)
ps (333 kb)
tex (134 kb)
References
- Aganagic M., Park J., Popescu C., Schwarz J.H., World-volume
action of the M theory five-brane, Nucl. Phys. B, 1997,
V.496, 191-214, hep-th/9701166.
- Ajith K.M., Harikumar E., Sivakumar M., Dual linearized gravity in
arbitrary dimensions, Class. Quant. Grav., 2005, V.22,
5385-5396, hep-th/0411202.
- Arcos H.I., Pereira J.G., Torsion gravity: a reappraisal,
Internat. J. Modern Phys. D, 2004, V.13, 2193-2240,
gr-qc/0501017.
- Arnowitt R., Deser S., Misner C.W., The dynamics of General
Relativity, in Gravitation: an Introduction to Current Research,
Editor L. Witten, New York, Wiley, 1962, 227-264, gr-qc/0405109.
- Bandos I., Berkovits N., Sorokin D., Duality-symmetric
eleven-dimensional supergravity and its coupling to M-branes,
Nucl. Phys. B, 1998, V.522, 214-233, hep-th/9711055.
- Bandos I., Lechner K., Nurmagambetov A., Pasti P., Sorokin D.,
Tonin M., Covariant action for super-five-brane of M theory,
Phys. Rev. Lett., 1997, V.78, 4332-4335, hep-th/9701149.
- Bandos I.A., Nurmagambetov A.J., Sorokin D.P., Various faces of
type IIA supergravity, Nucl. Phys. B, 2004, V.676, 189-228,
hep-th/0307153.
- Banks T., Landskepticism: or why effective potentials don't
count string models, hep-th/0412129.
- Bautier K., Deser S., Henneaux M., Seminara D., No cosmological
D=11 supergravity, Phys. Lett. B, 1997, V.406,
49-53, hep-th/9704131.
- Bekaert X., Boulanger N., Massless spin-two field S-duality,
Class. Quant. Grav., 2003, V.20, S417-S424, hep-th/0212131.
- Bekaert X., Boulanger N., Henneaux M., Consistent deformations of
dual formulations of linearized gravity: a no-go result,
Phys. Rev. D, 2003, V.67, 044010, 8 pages, hep-th/0210278.
- Bengtsson I., Kleppe A., On chiral p-forms, Int. J. Mod.
Phys. A, 1997, V.12, 3397-3412, hep-th/9609102.
- Bergshoeff E., Kallosh R., Ortin T., Roest D., Van Proeyen A.,
New formulation of D=10 supersymmetry and D8-O8 domain
walls, Class. Quant. Grav., 2001, V.18, 3359-3382,
hep-th/0103233.
- Berkovits N., Local actions with electric and magnetic sources,
Phys. Lett. B, 1997, V.395, 28-35, hep-th/9610134.
- Blau M., Killing vectors, constraints and conserved charges in
Kaluza-Klein theories, Class. Quant. Grav., 1987, V.4,
1207-1221.
- Borisov A., Ogievetsky V., Theory of dynamical affine and
conformal symmetries as gravity theory, Teoret. Mat. Fiz.,
1974, V.21, 329-342 (in Russian).
- Boulanger N., Cnockaert S., Henneaux M., A note on spin-s duality,
JHEP, 2003, V.0306, 060, 18 pages, hep-th/0306023.
- Brown J., Ganguli S., Ganor O.J., Helfgott C., E10 orbifolds,
JHEP, 2005, V.0506, 057, 60 pages, hep-th/0409037.
- Brown J., Ganor O.J., Helfgott C., M-theory and E10: billiards,
branes, and imaginary roots, JHEP, 2004, V.0408, 063, 68
pages, hep-th/0401053.
- Chan H.-M., Faridani J., Tsou S.T., Generalized dual symmetry for
non-Abelian Yang-Mills fields, Phys. Rev. D, 1996, V.53,
7293-7305, hep-th/9512173.
- Chaudhuri S., Hidden symmetry unmasked: matrix theory and E(11),
hep-th/0404235.
- Christensen S.M., Duff M.J., Quantizing gravity with a
cosmological constant, Nucl. Phys. B, 1980, V.170, 480-506.
- Cremmer E., Julia B., The SO(8) supergravity, Nucl. Phys. B,
1979, V.159, 141-212.
- Cremmer E., Julia B., Lü H., Pope C.N., Dualisation of dualities
I, Nucl. Phys. B, 1998, V. 523, 73-144, hep-th/9710119.
- Cremmer E., Julia B., Lü H., Pope C.N., Dualisation of dualities
II: Twisted self-duality of doubled fields and superdualities,
Nucl. Phys. B, 1998, V. 535, 242-292, hep-th/9806106.
- Cremmer E., Julia B., Scherk J., Supergravity theory in 11
dimensions, Phys. Lett. B, 1978, V.76, 409-412.
- Damour T., Cosmological singularities, billiards and Lorentzian
Kac-Moody algebras, gr-qc/0412105.
- Damour T., Cosmological singularities, Einstein billiards and
Lorentzian Kac-Moody algebras, gr-qc/0501064.
- Damour T., Henneaux M., Nicolai H., E10 and a "small tension
expansion" of M theory, Phys. Rev. Lett., 2002, V.89,
221601, 4 pages, hep-th/0207267.
- Damour T., Nicolai H., Higher order M theory corrections and the
Kac-Moody algebra E10, Class. Quant. Grav., 2005, V.22,
2849-2880, hep-th/0504153.
- de Andrade V.C., Barbosa A.L., Pereira J.G., Gravitation and
duality symmetry, gr-qc/0501037.
- Deser S., Drechsler W., Generalized gauge field copies, Phys.
Lett. B, 1979, V.86, 189-192.
- Deser S., Gibbons G.W., Born-Infeld-Einstein actions?, Class.
Quant. Grav., 1998, V.15, L35-L39, hep-th/9803049.
- Deser S., Jackiw R., t'Hooft G., Three-dimensional Einsten
gravity: dynamics of flat space, Ann. Phys., 1984, V.152,
220-235.
- Deser S., Jackiw R., Three-dimensional cosmological gravity:
dynamics of constant curvature, Ann. Phys., 1984, V.153,
405-416.
- Deser S., Jackiw R., Topologically massive gauge theories,
Ann. Phys., 1982, V.140, 372-411.
- Deser S., Nepomechie R.I., Electric-magnetic duality of conformal
gravitation, Phys. Lett. A, 1983, V.97, 329-332.
- Deser S., Seminara D., Free spin 2 duality invariance cannot be
extended to general relativity, Phys. Rev. D, 2005, V.71, 081502, 7 pages,
hep-th/0503030.
- Deser S., Teitelboim C., Duality transformations of Abelian and
non-Abelian gauge fields, Phys. Rev. D, 1976, V.13,
1592-1597.
- Deser S., Wilczek F., Non-uniqueness of gauge-field potentials,
Phys. Lett. B, 1976, V.65, 391-393.
- de Wit B., Nicolai H., Hidden symmetries, central charges and all
that, Class. Quant. Grav., 2001, V.18, 3095-3112,
hep-th/0011239.
- de Wit B., Nicolai H., Hidden symmetries in D=11
supergravity, Phys. Lett. B, 1985, V.155, 47-53.
- de Wit B., Nicolai H., D=11 supergravity with local SU(8)
invariance, Nucl. Phys. B, 1986, V.274, 363-400.
- Douglas M.R., Basic results in vacuum statictics, Comptes
Rendus Physique, 2004, V.5, 965-977, hep-th/0409207.
- Fradkin E.S., Gitman D.M., Shvartsman S.M., Quantum
electrodynamics with unstable vacuum, Berlin, Springer, 1991.
- Fradkin E.S., Tseytlin A.A., Quantum equivalence of dual field
theories, Ann. Phys., 1985, V.162, 31-48.
- Francia D., Hull C.M., Higher-spin gauge fields and duality,
hep-th/0501236.
- Fubini S., Veneziano G., Algebraic treatment of subsidiary
conditions in dual resonance model, Ann. Phys., 1971, V.63,
12-27.
- Gaberdiel M.R., Olive D.I., West P.C., A class of Lorentzian
Kac-Moody algebras, Nucl. Phys. B, 2002, V.645, 403-437,
hep-th/0205068.
- Garcia-Compean H., Obregon O., Plebansky J.F., Ramirez C., Towards
a gravitational analogue to S-duality in non-Abelian gauge
theories, Phys. Rev. D, 1998, V.57, 7501-7506,
hep-th/9711115.
- Garcia-Compean H., Obregon O., Ramirez C., Gravitational duality
in MacDowell-Mansouri gauge theory, Phys. Rev. D, 1998,
V.58, 104012, 3 pages, hep-th/9802063.
- Green M.B., Schwarz J.H., Witten E., Superstring theory,
Cambridge, Cambridge University Press, 1987.
- Gross D.J., High-energy symmetries of string theory, Phys.
Rev. Lett., 1988, V.60, 1229-1232.
- Henneaux M., Teitelboim C., Duality in linearized gravity,
Phys. Rev. D, 2005, V.71, 024018, 8 pages, gr-qc/0408101.
- Henry-Labordere P., Julia B., Paulot L., Borcherds symmetries in
M-theory, JHEP, 2002, V.0204, 049, 31 pages, hep-th/0212346.
- Henry-Labordere P., Julia B., Paulot L., Real Borcherds
superalgebras and M-theory, JHEP, 2003, V.0304, 060, 21 pages, hep-th/0203070.
- Hull C.M., Gravitational duality, branes and charges, Nucl.
Phys. B, 1998, V.509, 216-251, hep-th/9705162.
- Hull C.M., Strongly coupled gravity and duality, Nucl. Phys.
B, 2000, V.583, 237-259, hep-th/0004195.
- Hull C.M., Duality in gravity and higher spin gauge fields,
JHEP, 2001, V.0109, 027, 25 pages, hep-th/0107149.
- Hull C.M., Townsend P.K., Unity of superstring dualities,
Nucl. Phys. B, 1995, V.438, 109-137, hep-th/9410167.
- Iqbal A., Neitzke A., Vafa C., A mysterious duality, Adv.
Theor. Math. Phys., 2002, V.5, 769-808, hep-th/0111068.
- Julia B., Kac-Moody symmetry of gravitational and supergravity
theories, Lect. Appl. Math., 1985, V.21, 355-375.
- Julia B., Supergeometry and Kac-Moody algebras, in Vertex
Operators in Mathematics and Physics,
New York, Springer, 1985, 393-410
- Julia B., Levie J., Ray S., Gravitational duality near de Sitter
space, JHEP, 2005, V.0511, 025, 13 pages, hep-th/0507262.
- Kac V., Infinite dimensional Lie algebras, Birkhauser, Boston,
1983.
- Kaku M., Introduction to superstrings and M-theory, 2nd ed.,
Berlin, Springer, 1999.
- Koepsell K., Nicolai H., Samtleben H., An exceptional geometry for
d=11 supergravity?, Class. Quant. Grav., 2000, V.17,
3689-3702, hep-th/0006034.
- Linde A., Inflation and string cosmology, J. Phys. Conf.
Ser., 2005, V.24, 151-160, hep-th/0503195.
- Lü H., Pope C.N., Sezgin E., Stelle K.S., Stainless super
p-branes, Nucl. Phys. B, 1995, V.456, 669-698,
hep-th/9508042.
- Marcus N., Schwarz J.H., Field theories that have no manifestly
Lorentz-invariant formulation, Phys. Lett. B, 1982, V.115,
111-114.
- Martin I., Restuccia A., Duality symmetric actions and canonical
quantization, Phys. Lett. B, 1994, V.323, 311-315.
- Maznytsia A., Preitschopf C.R., Sorokin D.P., Duality of self-dual
actions, Nucl. Phys. B, 1999, V.539, 438-452,
hep-th/9805110.
- McClain B., Yu F., Wu Y.S., Covariant quantization of chiral
bosons and Osp(1|2) symmetry, Nucl. Phys.
B, 1990, V.343, 689-704.
- Mizoguchi S., E10 Symmetry in one-dimensional supergravity,
Nucl. Phys. B, 1998, V.528, 238-264, hep-th/9703160.
- Mkrtchyan H., Mkrtchyan R., Remarks on E11 approach,
hep-th/0507183.
- Moore G., Finite in all directions, hep-th/9305139.
- Nicolai H., D=11 supergravity with local SO(16)
invariance, Phys. Lett. B, 1987, V.187, 316-320.
- Nicolai H., A hyperbolic Lie algebra from supergravity, Phys.
Lett. B, 1992, V.276, 333-340.
- Nicolai H., Peeters K., Zamaklar M., Loop quantum gravity: an
outside review, Class. Quant. Grav., 2005, V.22, R193-R247, hep-th/0501114.
- Nicolai H., Warner N.P., The structure of N=16 supergravity in
two dimensions, Comm. Math. Phys., 1989, V.125, 369-384.
- Nieto J.A., S-duality for linearized gravity, Phys. Lett. A,
1999, V.262, 274-281, hep-th/9910049.
- Nurmagambetov A.J., On the sigma-model structure of type IIA
supergravity action in doubled field approach, JETP Lett.,
2004, V.79, 191-195, hep-th/0403100.
- Nurmagambetov A.J., Duality-symmetric gravity and supergravity:
testing the PST approach, hep-th/0407116.
- Obers N.A., Pioline B., U-duality and M-theory, Phys. Rep.,
1999, V.318, 113-225, hep-th/9809039.
- Ogievetsky V.I., Infinite-dimensional algebra of general
covariance group as the closure of finite dimensional algebras
of conformal and linear groups, Lett. Nuov. Cim., 1973, V.8,
988-990.
- Pasti P., Sorokin D.P., Tonin M., Note on manifest Lorentz and
general coordinate invariance in duality symmetric models,
Phys. Lett. B, 1995, V.352, 59-63, hep-th/9503182.
- Pasti P., Sorokin D.P., Tonin M., Duality symmetric actions with
manifest space-time symmetries, Phys. Rev. D, 1995, V.52,
4277-4281, hep-th/9506109.
- Pasti P., Sorokin D.P., Tonin M., On Lorentz invariant actions for
chiral p-forms, Phys. Rev. D, 1997, V.55, 6292-6298,
hep-th/9611100.
- Peldan P., Actions for gravity, with generalizations: a review,
Class. Quant. Grav., 1994, V.11, 1087-1132, gr-qc/9305011.
- Polchinski J., String theory, Cambridge, Cambridge University
Press, 1998.
- Pope C.N., Lectures on Kaluza-Klein,
http://faculty.physics.tamu.edu/pope/
- Salam A., Sezgin E., Supergravities in diverse dimensions, Vol. 1,
Singapore, World Scientific, 1989.
- Schnakenburg I., West P., Kac-Moody symmetries of IIB
supergravity, Phys. Lett. B, 2001, V.517, 421-428,
hep-th/0107181.
- Schnakenburg I., West P., Massive IIA supergravity as a non-linear
realisation, Phys. Lett. B, 2002, V.540, 137-145,
hep-th/0204207.
- Schwarz J.H., Sen A., Duality symmetric actions, Nucl. Phys.
B, 1994, V.411, 35-63, hep-th/9304154.
- Sorokin D., Lagrangian description of duality-symmetric fields,
in Advances in the Interplay between Quantum and Gravity Physics,
Editors P.G. Bergmann and V. de Sabbata, Kluwer Academic Pub.,
2002, 365-385.
- Schrödinger E., Space-time structure, Cambridge Univ. Press,
1950.
- Susskind L., The anthropic landscape of string theory,
hep-th/0302219.
- Thirring W., A course on mathematical physics, Vol. 2, Field
theory, 2nd ed., Berlin, Springer, 1986.
- Townsend P.K., The eleven-dimensional supermembrane revisited,
Phys. Lett. B, 1995, V.350, 184-187, hep-th/9501068.
- Virasoro M.A., Subsidiary conditions and ghosts in dual-resonance
model, Phys. Rev. D, 1970, V.1, 2933-2936.
- West P., Hidden superconformal symmetry in M theory, JHEP,
2000, V.0008, 007, 21 pages, hep-th/0005270.
- West P., E11 and M theory, Class. Quant.
Grav., 2001, V.18, 4443-4460, hep-th/0104081.
- West P., Very extended E8 and A8 at low
levels, gravity and supergravity, Class. Quant. Grav., 2002,
V.20, 2393-2406, hep-th/0212291.
- Witten E., 2+1 dimensional gravity as an exactly soluble system,
Nucl. Phys. B, 1988/89, V.311, 46-78.
- Witten E., String theory dynamics in various dimensions,
Nucl. Phys. B, 1995, V.443, 85-126, hep-th/9503124.
- Wotzasek C., The Wess-Zumino term for chiral bosons, Phys.
Rev. Lett., 1991, V.66, 129-132.
- Wu T.T., Yang C.N., Some remarks about unquantized non-Abelian
gauge fields, Phys. Rev. D, 1975, V.12, 3843-3844.
- Zwanziger D., Local Lagrangian quantum field theory of electric
and magnetic charges, Phys. Rev. D, 1971, V.3, 880-890.
|
|