Five-dimensional supergravity and the hyperbolic Kac–Moody algebra GH2

Motivated by the recent analysis of the E10 sigma model for the study of M-theory, we study a one-dimensional sigma model associated with the hyperbolic Kac–Moody algebra GH2 and its link to pure supergravity, which closely resembles in many ways D = 11 supergravity. The bosonic equations of motion and the Bianchi identity for D = 5 pure supergravity match the equations of the level ℓ ⩽ 3 truncation of the GH2 sigma model up to higher level terms, just as they do for the D = 11 case. We also compute low level root and outer multiplicities in the A3 decomposition, and indeed find singlets at ℓ = 4k, k = 2, 3, … corresponding to the scaling of ERk+1 terms, although the missing singlet at ℓ = 4 remains a puzzle.

[1]  P. Vanhove,et al.  Duality and higher derivative terms in M theory , 2005, hep-th/0510027.

[2]  H. Nicolai.  Gravitational Billiards, Dualities and Hidden Symmetries , 2005, gr-qc/0506031.

[3]  T. Damour,et al.  Higher-order M-theory corrections and the Kac–Moody algebra E10 , 2005, hep-th/0504153.

[4]  M. Henneaux,et al.  From very-extended to overextended gravity and M-theories , 2004, hep-th/0412184.

[5]  H. Nicolai,et al.  IIB supergravity and E10 , 2004, hep-th/0411225.

[6]  T. Damour,et al.  Eleven dimensional supergravity and the E(10)/E(E10) sigma-model at low A(9) levels , 2004, hep-th/0410245.

[7]  H. Nicolai,et al.  E10 and SO(9, 9) invariant supergravity , 2004, hep-th/0407101.

[8]  F. Englert,et al.  G+++ Invariant formulation of gravity and M-theories: exact intersecting brane solutions , 2004, hep-th/0405082.

[9]  O. Ganor,et al.  M-theory and E10: Billiards, Branes, and Imaginary Roots , 2004, hep-th/0401053.

[10]  F. Englert,et al.  G+++ invariant formulation of gravity and M theories: Exact BPS solutions , 2003, hep-th/0311255.

[11]  P. West,et al.  Very extended Kac Moody algebras and their interpretation at low levels , 2003, hep-th/0309198.

[12]  H. Nicolai,et al.  Low level representations for E(10) and E(11) , 2003, hep-th/0301017.

[13]  T. Damour,et al.  TOPICAL REVIEW: Cosmological billiards , 2002 .

[14]  T. Damour,et al.  E10 and a small tension expansion of m theory. , 2002, Physical review letters.

[15]  T. Damour,et al.  Einstein billiards and overextensions of finite-dimensional simple Lie algebras , 2002, hep-th/0206125.

[16]  S. Mizoguchi.  On asymmetric orbifolds and the D=5 no-modulus supergravity , 2001, hep-th/0109193.

[17]  P. West.  E11 and M theory , 2001, hep-th/0104081.

[18]  T. Damour,et al.  Hyperbolic Kac Moody Algebras and Chaos in Kaluza Klein Models , 2001, hep-th/0103094.

[19]  T. Damour,et al.  E10, BE10 and arithmetical chaos in superstring cosmology. , 2000, Physical review letters.

[20]  Damour,et al.  Chaos in superstring cosmology , 2000, Physical review letters.

[21]  S. Mizoguchi,et al.  On discrete U duality in M theory , 1999, hep-th/9909150.

[22]  S. Penati,et al.  Two point functions of chiral operators in N=4 SYM at order g**4 , 1999, hep-th/9910197.

[23]  J. Harvey,et al.  String Islands , 1998, hep-th/9809122.

[24]  N. Ohta,et al.  More on the similarity between D=5 simple supergravity and M theory , 1998, hep-th/9807111.

[25]  S. Mizoguchi.  E10 SYMMETRY IN ONE-DIMENSIONAL SUPERGRAVITY , 1997, hep-th/9703160.

[26]  L. Susskind,et al.  M theory as a matrix model: A Conjecture , 1996, hep-th/9610043.

[27]  S. Ferrara,et al.  Low-energy analysis of M and F theories on Calabi-Yau threefolds , 1996, hep-th/9604097.

[28]  S. Ferrara,et al.  M-theory on a Calabi-Yau manifold , 1996, hep-th/9602102.

[29]  M. Duff,et al.  Eleven-dimensional origin of string-string duality: A One loop test , 1995, hep-th/9506126.

[30]  E. Witten,et al.  A one-loop test of string duality , 1995, hep-th/9505053.

[31]  Melnikov,et al.  Dynamics of inhomogeneities of the metric in the vicinity of a singularity in multidimensional cosmology. , 1994, Physical review. D, Particles and fields.

[32]  V. Ivashchuk,et al.  Billiard representation for multidimensional cosmology with multicomponent perfect fluid near the singularity , 1994, gr-qc/9407028.

[33]  C. Misner.  The Mixmaster Cosmological Metrics , 1994, gr-qc/9405068.

[34]  M. Henneaux,et al.  Are Kaluza-Klein models of the universe chaotic? , 1989 .

[35]  M. Henneaux,et al.  Non-oscillatory behaviour in vacuum Kaluza-Klein cosmologies , 1985 .

[36]  J. Schwarz,et al.  Three-Dimensional Supergravity Theories , 1983 .

[37]  E. Fradkin,et al.  Quantum Properties of Higher Dimensional and Dimensionally Reduced Supersymmetric Theories , 1983 .

[38]  V. Belinskiǐ,et al.  A General Solution of the Einstein Equations with a Time Singularity , 1982 .

[39]  H. Nicolai,et al.  Coupling the SO(2) supergravity through dimensional reduction , 1980 .

[40]  E. Cremmer,et al.  Supergravity in theory in 11 dimensions , 1978 .

[41]  I. Stewart,et al.  Infinite-dimensional Lie algebras , 1974 .

[42]  V. Belinskiǐ,et al.  Oscillatory approach to a singular point in the relativistic cosmology , 1970 .