Algebraic Structures in M-theory
Typ
Examensarbete för masterexamen
Master Thesis
Master Thesis
Program
Publicerad
2004
Författare
Bao, Ling
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
In this thesis we reformulate the bosonic sector of eleven dimensional supergravity as a simultaneous nonlinear realisation based on the conformal group and an enlarged affine group called G_{11}. The vielbein and the gauge fields of the theory appear as space-time dependent parameters of the coset representatives. Inside the corresponding algebra g_{11} we find the Borel subalgebra of e_7, whereas performing the same procedure for the Borel subalgebra of e_8 we have to add some extra generators. The presence of these new generators lead to a new formulation of gravity, which includes both a vielbein and its dual. We make the conjecture that the final symmetry of M-theory should be described by a coset space, with the global and the local symmetry given by the Lorentzian Kac-Moody algebra e_{11} and its subalgebra invariant under the Cartan involution, respectively. The pure gravity itself in $D$ dimensions is argued to have a coset symmetry based on the very extended algebra A^{+++}_{D-3}. The tensor generators of a very extended algebra are divided into representations of its maximal finite dimensional subalgebra. The space-time translations are thought to be introduced as weights in a basic representation of the Kac-Moody algebra. Some features of the root system of a general Lorentzian Kac-Moody algebra are discussed, in particular those related to even self-dual lattices.
Beskrivning
Ämne/nyckelord
Fysik , Physical Sciences