6533b861fe1ef96bd12c4161

RESEARCH PRODUCT

Symmetry and holonomy in M Theory

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Eleven-dimensional M Theory is conjectured to contain and unify quantum gravity and the rest of fundamental interactions. Despite its current lack of a precise formulation, hints and information about M Theory can be retrieved from its low energy limit, eleven-dimensional supergravity. In fact, this Thesis aims to make progress towards the understanding of M Theory by the study of eleven dimensional supergravity. Two important questions in M Theory yet to be solved are 1) how many supersymmetries can an M Theory background preserve and 2) what is the symmetry of M Theory. Both questions are addressed in this Thesis at the D=11 supergravity level.The former question can be studied for purely bosonic solutions by means of generalized holonomy, namely, the holonomy of the supersymmetric connection defining the supersymmetry variation of the gravitino. The role of generalized holonomy in this context is reviewed, and successive covariant derivatives of the curvature of the supersymmetry connection are shown to be necessary to properly define the generalized holonomy algebra.As for the later, the underlying gauge group structure of D=11 supergravity becomes manifest when its three-form field A_3 is expressed through a set of one-form gauge fields, associated with the generators of a family of enlarged supersymmetry algebras (which are fermionic extensions of the M Theory superalgebra). The problem can be tackled by trivializing a standard supersymmetry algebra Chevalley-Eilenberg four-cocycle (associated to dA_3) on the enlarged superalgebras. The family of trivializing superalgebras are related to osp(1|32) through "expansion", a method to obtain new Lie (super)algebras of increasing dimensions from given ones, that is also discussed.This analysis of the underlying gauge symmetry of D=11 supergravity leads naturally to enlarged supersymmetry algebras and superspaces making, thus, natural to consider actions for objects moving in such spaces. In particular, a string moving in tensorial space is discussed, describing the excitations of a state preserving 30 out of 32 supersymmetries (hence composed of two preons, hypothetical constituents of M Theory preserving 31 supersymmetries). A G-frame method is also discussed to study hypothetical preonic solutions of supergravity.