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## VII. Branes

### Branes and dualities

In the previous chapter we saw that different string theories are connected by dualities. A closed string theory on a circle, it turned out, is equivalent to a closed string theory on a circle of inverse radius. A natural question to ask then is: what is the T-dual of an open string theory on a circle ?

The answer turns out to be very interesting. In the theory T-dual to the open string theory on the circle, we find only closed strings everywhere, but we find that the open strings are now restricted to live on objects called branes. The open strings cannot freely move everywhere in space anymore, but their endpoints are confined to move on these branes. In generalizing T-duality, we discover new objects in string theory, called branes, that can have any dimension we want. Indeed, upon performing further T-dualities, it turns out that the open string endpoints are more and more confined to live on branes of smaller and smaller dimension. Thus we find objects in string theories that are not strings. The branes that we find can have dimension 0 (points), 1 (stringlike branes), 2 (membranes), 3 (volumes, like the space we live in), and even higher dimensions, up to nine, since otherwise they wouldn't fit into our nine-dimensional space anymore. These are new objects in string theory, and they allow for amazing new possibilities.

### A world of light

Since a brane is an object on which open strings live, we can expect to find a gauge field living on a brane. Moreover, if only closed string modes live in the whole of the space, we expect gravitons in the whole of the space, on the brane and in the rest of the space. This leads to a new possibility for the answer to the question we posed some time ago: where are the six extra dimensions of string theory ?

Assume that we have a brane that is three-dimensional, just like our space. Then we would have gauge fields living on the brane, in three spatial dimensions. That brane could look exactly like our world if the gauge fields and particles would be like the ones in the Standard Model. In other words, our world just might be such a three-dimensional brane. And since, say, the photon only lives on the brane, all the other six dimensions would be literally dark. Indeed, no photons, or light, would come from these other dimensions, and no light would leak into these dimensions, since the photons (gauge fields) can only live on the brane.

### Brane new world

Of course we would still 'see' the extra dimensions through particles interacting with the gravitons that do still live in all 9 dimensions, but the effects of the gravitons living in these extra dimensions can be so small that we actually even can have extremely large extra dimensions without 'seeing' them through gravitational forces. The gravitational force is simply too weak to make us able to see these extra dimensions.

Actually, these extra dimensions can be as large as a tenth of a millimeter without us being able to seem them at this moment. Experiments are now being done that would allow us to see extra dimensions that are as big as a tenth of a millimeter, but since they involve the very weak gravitational force, the experiments are technically very involved -- everybody would be thrilled if we could see deviations in the gravitational force due to the existence of extra dimensions.