| The vacuum structure of some field and string theories is investigated.; In Section I we calculate the energy level shifts of a Rydberg atom caused by the vacuum fluctuations of the electric field between two neutral conducting plates, and numerical values for the shifts of the lowest levels are given. We also build a primitive model of the spontaneous breakdown of chiral symmetry for confined fermions. Exact expressions for the fermion condensate and the vacuum stress are obtained.; In Section II we derive the propagator and one-loop effective potential for a scalar field in an n-dimensional Anti-deSitter background. We show that the direct mode sum gives a physically reasonable potential which disagrees with the one obtained by analytic continuation from the n-sphere. We also find the two-point functions for spinors on maximally symmetric spaces in four functions for spinors on maximally symmetric spaces in four dimensions, and show that chiral symmetry is broken in AdS with supersymmetric boundary conditions.; In Section III we calculate the one-loop effective potential of eleven dimensional supergravity, prove graviton dominance and show that this model does not admit a flat space solution with a spherical compact sector, at least not when the Freund-Rubin parameter vanishes.; Finally, in Section IV we develop tools for obtaining phenomenology from ten dimensional theories. The Z-manifold is described in detail, we discuss some properties of Calabi-Yau manifolds of complete intersection and we show that the octets usually exist but never couple on these manifolds. |
