Massive String Modes Research Articles

Superstring gravity and the early universe

Ten-dimensional superstring theories have been proposed as candidates for a unified description of all the forces of nature. These theories reduce to Einstein gravity coupled to Yang-Mills interactions at energy scales small compared to the string tension. The phenomenologically promising superstring theory, the heterotic string, is investigated at the high temperatures and short distances relevant in the early universe. The massive string modes alone constitute an unstable thermodynamic system with negative specific heat. The conditions for equilibrium between the massive string modes and the massless modes (radiation) are derived. The large energy fluctuations of the system require the use of the microcanonical ensemble. There is a maximum temperature which exceeds the temperature at which the canonical partition function becomes divergent. Above a critical volume there is a phase transition during which the massive string modes must evaporate. The possibilities of spontaneous compactification, large entropy production, and a solution of the horizon and flatness problems are discussed.

Superstring field theory

Superstring field theories are formulated in terms of light-cone-gauge superfields that are functionals of string coordinates x( σ) and ϑ( σ). The formalism used preserves only the manifest SU(4) symmetry that corresponds to rotations among six of the eight transverse directions. In type I theories, which have one ten-dimensional supersymmetry and describe both open and closed strings, there are five interaction terms of two basic kinds. One kind is a breaking or joining interaction, which is a string generalization of a cubic Yang-Mills coupling. It is relevant to both the three open-string vertex and the open-string to closed-string transition vertex. The other kind is an exchange or crossing-over interaction, which is a string generalization of a cubic gravitational coupling. All the interactions can be uniquely determined by requiring continuity of the coordinates x( σ) and ϑ( σ) (which implies local conservation of the conjugate momenta) and by imposing the global supersymmetry algebra. Specific local operators are identified for each of the two kinds of interactions. In type II theories, which have two ten-dimensional supersymmetries and contain closed strings only, the entire interaction hamiltonian consists of a single cubic vertex. The higher-order contact terms of the N = 8 supergravity theory that arises in the low-energy limit give an effective description of the exchange of massive string modes.