Frontier physics

Bosonic string theory and superstrings

One-dimensional strings vibrate into a particle spectrum; quantum consistency constrains dimensionality and theory structure.

Replace point-particle trajectories with finite-length strings. Open and closed strings have distinct vibration modes; the closed-string spectrum includes a massless spin-2 mode, a graviton candidate. This is a mathematical feature, not experimental evidence for fundamental strings.

Quantization and supersymmetry

Quantizing a string produces a tower of states whose masses depend on oscillator level. The bosonic string is consistent in 26 spacetime dimensions but has a tachyon in its spectrum. Superstrings add worldsheet fermions, remove the tachyon in consistent models, and typically require 10 dimensions; six may be compactified.

At low energy, the massless spin-2 mode of a closed string behaves as a graviton, while heavier excitations form a tower set by the string scale. If a compact dimension has radius $R$, T-duality relates it to $\alpha’/R$ and exchanges momentum with winding modes. This is a striking internal consistency, but it does not uniquely select the compact geometry or the particle spectrum of nature.

The string spectrum depends on boundary conditions, topology, and compactification, so different solutions can lead to different effective physics. Supersymmetry removes some instabilities of the bosonic theory but does not by itself select a vacuum or connect it to data. A meaningful consistency test is to derive the effective laws and ask whether they recover classical gravity and known matter at accessible energies.