Aspects of Tachyon Condensation in String Theory: The Open and Closed Cases

A nonperturbative formulation of M/String theory is lacking. One phenomenon necessarily sensitive to the underlying nonperturbative dynamics is vacuum decay. Tachyonic fluctuations in perturbative string theories indicate an instability of the vacuum. We investigate aspects of tachyon condensation in both the open and closed sectors of string theory. In the case of open string tachyons we review and extend the construction of unstable D-branes as noncommutative solitons. This incorporates techniques from noncommutative field theory, string field theory, and an important conjecture due to Sen. We also extend this discussion to actions consistent with T-duality and comment on a technique developed to generate soliton solutions. For the case of closed strings we conjecture that the end point of tachyon condensation, at any non-zero coupling, involves the annihilation of space time by a bubble of nothing, resulting in a topological phase of the theory. In support of this we present a variety of situations in which there is a correspondence between the existence of perturbative tachyons in one regime and the semi-classical annihilation of space-time. Our discussion will include many supersymmetry breaking scenarios in string theory including Scherk-Schwarz compactifications, Melvin magnetic backgrounds, and noncompact orbifolds. We use this conjecture to investigate a possible web of dualities relating the eleven-dimensional Fabinger-Horava background to nonsupersymmetric string theories. Along the way we point out where our conjecture resolves some of the puzzles associated with bulk closed string tachyon condensation. We finally discuss the implications of these analyses to a nonperturbative formulation of M-theory. Included as an appendix is a discussion of the use of T-duality to map the conditions for supersymmetry preservation in Dbrane systems at angles to analogous conditions on background magnetic fields. We also discuss T-dual versions of noncommutative tachyon decays resolving some ambiguities therein