Rather than strings, fundamental elements can be membranes {supermembrane} {2-brane} {3-brane} {p-brane}|, of dimension 2, 3, or any natural number p. Minimum length is Planck length. Branes vibrate and have high-energy waves. Branes require ten space dimensions (three infinite and seven curled up) and one time dimension.
Open-string endpoints can stay fixed at one point (Dirichlet boundary condition) (zero-dimension brane), which maintains vacuum gauge invariance. Endpoints can move along straight or curved lines (Neumann boundary condition) (one-dimension brane), which fixes particles. Endpoints can move around surfaces (two-dimension brane) or higher branes.
Physical Sciences>Physics>String Theory>Brane
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Date Modified: 2022.0224