A space or structure in M-Theory, the new theory of the nature of the universe. The name comes from membrane, and is a generalisation of a string in string theory. A string is one-dimensional, a membrane is a two-dimensional surface, and a p-brane is a space of any dimension p. So the general term is brane.

M-Theory says that no one way of looking at the universe, like points or strings, is the true way, but higher symmetries become apparent when you move to higher dimensions, and there is no exact number of dimensions that you can't go beyond. (That's my understanding at any rate.)

A new theory of the Big Bang called the ekpyrotic universe model says that the energy release of the Big Bang came about from the collision of two 3-branes in something called bulk space.

Superstrings can have various kinds of boundary conditions, which limit their behaviour. When the strings are 'open', that is not closed loops, they can have two kinds of boundary conditions, Neumann and Dirichlet. With the Neuman boundary condition, one end point is fixed into some manifold, and the other is free to move about, however no momentum flows out of this system. With the Dirichlet boundary condition, the ends are fixed into the manifold, and can only move within this manifold.

The manifold is known as a D-brane, or more generally as a Dp-brane where p is an integer ranging from -1 to the number of spatial dimensions in the space-time you're looking at! So for the 10 dimensional superstring theories, you can have up to D9-branes. The -1 brane refers to a kind of null state, where the space and time coordinates are fixed. D0-branes are point like, D1-branes are string like, D2-branes are like bounded membranes, D3-branes are like soap bubbles, and past there, I don't know how to visualise. Presumably they have the same kinds of geometry of higher dimensional solids such as the hypercube and hypersphere.

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