The structure of E(10) at higher A(9) levels: a first algorithmic approach
The structure of E(10) at higher A(9) levels: a first algorithmic approach
The conjecture of a hidden E10 symmetry of M-theory is supported by the close connection between the dynamics of D = 11 supergravity near a spacelike singularity and a truncation of an one-dimensional ?-model with E10 symmetry where all representations beyond SL(10) level ell = 3 are omitted. If this conjecture is right, higher-level representations should especially capture the dynamics of further M-theory degrees of freedom. Unfortunately, the level by level determination of E10 commutators which is necessary to extend the model to higher levels is both an involved and toilsome task that requires computer aid. In this work, some of the relevant problems are exposed and algorithmic methods are developed which simplify key steps in the determination of explicit E10 commutators at higher levels. As an application, we compute the commutator of the level-two six-form with itself
m-theory, kac-moody algebras, fundamental symmetries
1-24
Fischbacher, Thomas
d3282f31-0a6a-4d19-80d0-e3bebc12f67a
August 2005
Fischbacher, Thomas
d3282f31-0a6a-4d19-80d0-e3bebc12f67a
Fischbacher, Thomas
(2005)
The structure of E(10) at higher A(9) levels: a first algorithmic approach.
Journal of High Energy Physics, JHEP08(2005)012, .
(doi:10.1088/1126-6708/2005/08/012).
Abstract
The conjecture of a hidden E10 symmetry of M-theory is supported by the close connection between the dynamics of D = 11 supergravity near a spacelike singularity and a truncation of an one-dimensional ?-model with E10 symmetry where all representations beyond SL(10) level ell = 3 are omitted. If this conjecture is right, higher-level representations should especially capture the dynamics of further M-theory degrees of freedom. Unfortunately, the level by level determination of E10 commutators which is necessary to extend the model to higher levels is both an involved and toilsome task that requires computer aid. In this work, some of the relevant problems are exposed and algorithmic methods are developed which simplify key steps in the determination of explicit E10 commutators at higher levels. As an application, we compute the commutator of the level-two six-form with itself
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Submitted date: 17 May 2005
Published date: August 2005
Keywords:
m-theory, kac-moody algebras, fundamental symmetries
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Local EPrints ID: 46370
URI: http://eprints.soton.ac.uk/id/eprint/46370
PURE UUID: 206fa0b3-da2f-4f06-98fe-9c455891bc98
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Date deposited: 22 Jun 2007
Last modified: 15 Mar 2024 09:21
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Author:
Thomas Fischbacher
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