M-Theory ; The Grand Masterpiece

There are five different superstring theories, each ten-dimensional, all seemingly incompatible. But in 1995, Edward Witten proposed that the five theories were actually all part of a large, mysterious and uncharted framework that he dubbed M-theory.

We don’t have the full equations for M-theory, but there are many hints as to how it works. Witten showed that the five theories are linked to each other via dualities: one formulation at strong coupling is identical to another at weak coupling. M-theory is the complete skeleton whilst the five superstring models are individual bones.

M-theory doesn’t have ten spacetime dimensions, but eleven – ten space and one time! Now there isn’t a string theory in eleven dimensions, but there is a supersymmetric theory of gravity, calledsupergravity. Witten showed that there was a continuous path between the ten-dimensional string theories and the eleven-dimensional theory of supergravity; supergravity is part of the M-theory web.

Our understanding of M-theory is by no means complete. It seems to be the single unifying structure into which all string theories fit. Dualities allow us to relate some of the fringes, where interactions are very weak or very strong. But the middle of the web remains impenetrable.

Some of the duality calculations are surprising, and impressive. Nonetheless we can only see the edges of the picture, and we grasp little of its mathematics. We have yet to derive any concrete predictions and experimental evidence of the required extra dimensions remains elusive. Like an artistic masterpiece with a hole through the middle, it gives us a tantalising glimpse of what might be the ultimate unifying theory

D-Branes

M-theory is not just populated by strings, but also by membranes called D-branes. These are multi-dimensional surfaces that move through the eleven dimensions of M-theory. We can have D-branes of up to nine spatial dimensions (though that’s a little hard to visualise)! A point is a D0-brane, a string a D1-brane, a sheet a D2-brane and so on.

Eleven-dimensional M-theory can look exactly like ten-dimensional string theory. This happens when one of the eleven dimensions is extremely small and circular. A two-dimensional D-brane wrapped around this extra dimension will look like a cylinder. But if the circular dimension is tiny then this cylinder will be very thin. As a result the D-brane will appear to be a one-dimensional string moving in ten dimensions (see picture).

In recent years D-branes have become increasingly important to research. They are natural places for fixed endpoints of open strings to live. And strings living on D-branes give rise to the same kind of forces that appear in the Standard Model.

But there is an even more potent reason driving interest in D-branes: they are non-perturbative objects. D-branes allow physicists to do calculations that transcend the approximate methods of perturbation theory. Thus we can uncover elements of the theory in regimes where interactions are strong. Historically this was uncharted terrain.

D-branes are a central ingredient in modern research. They can be used to construct cosmological models within string theory. Researchers in brane cosmology build models of inflation based on brane collisions. And the study of D-branes has shed light on some of the most elusive elements in the universe, black holes. Finally, D-branes played an essential role in formulating the AdS/CFT correspondence.

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