On M-Theory

This contribution gives a personal view on recent attempts to find a unified framework for non-perturbative string theories, with special emphasis on the hidden symmetries of supergravity and their possible role in this endeavor. A reformulation of $d=11$ supergravity with enlarged tangent space symmetry SO(1,2) $\times$ SO(16) is discussed from this perspective, as well as an ansatz to construct yet further versions with SO(1,1) $\times$ SO(16)$^\infty$ and possibly even SO(1,1)$_+$ $\times$ ISO(16)$^\infty$ tangent space symmetry. It is suggested that upon ``third quantization'', dimensionally reduced maximal supergravity may have an equally important role to play in this unification as the dimensionally reduced maximally supersymmetric $SU(\infty)$ Yang Mills theory.Comment: 16 pages (Latex), contribution to the 31st Ahrenshoop International Symposium on the Theory of Elementary Particles, Buckow, Germany, 2-6 September 1997, and the Discussion Meeting on Black Holes, Bangalore, India, 8-10 December 1997. Changes in section 4, minor corrections in previous section

Boundaries in M-Theory

We formulate boundary conditions for an open membrane that ends on the fivebrane of {\cal M}-theory. We show that the dynamics of the eleven-dimensional fivebrane can be obtained from the quantization of a ``small membrane'' that is confined to a single fivebrane and which moves with the speed of light. This shows that the eleven-dimensional fivebrane has an interpretation as a $D$-brane of an open supermembrane as has recently been proposed by Strominger and Townsend. We briefly discuss the boundary dynamics of an infinitely extended planar membrane that is stretched between two parallel fivebranesComment: 16 pages, phyzz

E_11 and M Theory

We argue that eleven dimensional supergravity can be described by a non-linear realisation based on the group E_{11}. This requires a formulation of eleven dimensional supergravity in which the gravitational degrees of freedom are described by two fields which are related by duality. We show the existence of such a description of gravity.Comment: 21 pages, some typos corrected and two references adde

Basics of M-Theory

This is a review article of eleven dimensional supergravity in which we present all necessary calculations, namely the Noether procedure, the equations of motion (without neglecting the fermions), the Killing spinor equation, as well as some simple and less simple supersymmetric solutions to this theory. All calculations are printed in much detail and with explicit comments as to how they were done. Also contained is a simple approach to Clifford algebras to prepare the grounds for the harder calculations in spin space and Fierz identities.Comment: 96 pages, corrected and extended versio

On topological M-theory

We construct a gauge fixed action for topological membranes on $G_2$-manifold such that its bosonic part is the standard membrane theory in a particular gauge. We prove that quantum mechanically the path-integral in this gauge localizes on associative submanifolds. Moreover on $M\times S^1$ the theory naturally reduces to the standard A-model on Calabi-Yau manifold and to a membrane theory localized on special Lagrangian submanifolds. We discuss some properties of topological membrane theory on $G_2$-manifolds. We also generalize our construction to topological $p$--branes on special manifolds by exploring a relation between vector cross product structures and TFTs.Comment: 20 page

M-theory dark matter

The phenomenological implications of the eleven dimensional limit of $M$-theory (strongly coupled $E_8\times E_8$) are investigated. In particular we calculate the supersymmetric particle spectrum subject to constraints of correct electroweak symmetry breaking and the requirement that the lightest supersymmetric particle provides the dark matter of the universe. We also calculate direct detection event rates of the lightest neutralino relevant for non-baryonic dark matter experiments. The modulation effect, due to Earth's annual motion is also calculated.Comment: LaTeX file, 30 pages including 12 figures;v2 typos fixed and references adde