Physics through extra dimensions: On dualities, unification, and pair production

This thesis has two parts. In the first part we study M-theory compactifications on singular manifolds of G₂ holonomy which are asymptotic to quotients of cones over S3 x S3. We investigate the moduli space of M-theory compactifications on these manifolds, and we discover smooth interpolations leading to a new kind of duality among four dimensional supersymmetric gauge theories with different gauge groups, with a fixed number of abelian factors. The quotients are such that the internal space has a finite, non-trivial fundamental group, and we construct a grand unified model in which the breaking of the gauge symmetry by Wilson lines to the standard model arises naturally. This model provides the basis for the study of unification from M-theory. Contrary to long-standing perception, we show that a grand unification scale exists even in the presence of threshold corrections. We obtain a precise relation between the unification scale and the mass of heavy gauge bosons in terms of topological invariants. This relation replaces the often-made assumption that the unification scale and the heavy masses are equal. We also find the relation between Newton's constant, the unification scale, and the unified couplings. We go on to investigate the lifetime of the proton and we find that, when compared with standard four dimensional GUT'S, some modes of proton decay in M-theory compactifications are suppressed relative to others.; In the second part of the thesis, we combine two rather fundamental, yet previously disjoint, results: one is the Kaluza-Klein unification of gravity with electromagnetism via the introduction of an extra dimension; the other is Schwinger's production of electron-positron pairs from a constant electric field. The combination involves investigating the production of pairs of KK-charged particles from a KK electric field. While it has been well-accepted that Schwinger pair production occurs via a semi-classical tunneling mechanism, we find here that pair production takes place even though tunneling does not. Instead, the pair production occurs via a different mechanism which involves a combination of the Unruh effect and vacuum polarization.