Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1997-03-25
Physics
High Energy Physics
High Energy Physics - Theory
18 pages, Latex no figures, improved treatment of reduced sector
Scientific paper
A Chern-Simons theory in 11 dimensions, which is a piece of the 11 dimensional supergravity action, is considered as a quantum field theory in its own right. We conjecture that it defines a non-perturbative phase of M theory in which the metric and gravitino vanish. The theory is diffeomorphism invariant but not topological in that there are local degrees of freedom. Nevertheless, there are a countable number of momentum variables associated with relative cobordism classes of embeddings of seven dimensional manifolds in ten dimensional space. The canonical theory is developed in terms of an algebra of gauge invariant observables. We find a sector of the theory corresponding to a topological compactification in which the geometry of the compactified directions is coded in an algebra of functions on the base manifold. The diffeomorphism invariant quantum theory associated to this sector is constructed, and is found to describe diffeomorphism classes of excitations of three surfaces wrapping homology classes of the compactified dimensions.
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