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In theoretical physics, a membrane, brane, or p-brane is a spatially extended mathematical concept that appears in string theory and related theories (e.g. M-theory and brane cosmology). The membrane exists in a static number of dimensions.
The variable p refers to the number of spatial dimensions of the brane. That is, a 0-brane is a zero-dimensional pointlike particle, a 1-brane is a string, that can either be open or closed, a 2-brane is a "membrane", etc. Every p-brane sweeps out a (p+1)-dimensional world volume as it propagates through spacetime.
Originally string theory was a theory of 1-branes called strings. By the mid-1990s, it became apparent that the theory could be extended to include higher dimensional objects also. Typically these objects are non-perturbative features of the theory (meaning they do not appear in perturbation theory).
Besides the fundamental string (or F-string) of string theory and its magnetic dual, the NS5-brane, the most important type of branes that appear are the D-branes. Different types of D-branes appear in different theories. Dn-branes with even n appear in type IIA string theory whereas the odd Dp-branes appear in type IIB string theory.
With the development of M-theory, an extra dimension appeared and the fundamental string of string theory became a 2-dimensional membrane called an M2-brane (or supermembrane). Its magnetic dual is an M5-brane. The various branes of string theory are thought to be related to these higher dimensional M5-branes wrapped on various cycles.
The M-theory states that strings of energy could grow into larger membranes or branes even up to the size of the universe.
It also goes on to state that these strings need to vibrate in more than three dimensions (six) plus another dimension – time.
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